Updated on 2024/02/15

写真a

 
TAKAOKA Koichiro
 
Organization
Faculty of Commerce Professor
Other responsible organization
Commerce Course of Graduate School of Commerce, Master's Program
Commerce Course of Graduate School of Commerce, Doctoral Program
Contact information
The inquiry by e-mail is 《here
External link

Degree

  • 博士(数理科学) ( 東京大学 )

  • 修士(数理科学) ( 東京大学 )

Education

  • 1995.3
     

    The University of Tokyo   master course   completed

  • 1993.3
     

    The University of Tokyo   graduated

  • 1989.3
     

    国立筑波大学附属駒場高等学校   graduated

Research History

  • 2019.4 - Now

    Professor, Faculty of Commerce, Chuo University

  • 2019.10    

    京都大学大学院理学研究科非常勤講師

  • 2018.4 - 2019.3

    一橋大学大学院経営管理研究科教授

  • 2015.4 - 2018.3

    一橋大学大学院商学研究科教授

  • 2017.1    

    大阪大学大学院基礎工学研究科非常勤講師

  • 2007.4 - 2015.3

    一橋大学大学院商学研究科准教授

  • 2012.10 - 2013.1

    東京大学大学院経済学研究科非常勤講師

  • 2010.10    

    千葉大学理学部非常勤講師

  • 2009.10    

    首都大学東京理学部非常勤講師

  • 2009.6 - 2009.7

    京都大学大学院理学研究科非常勤講師

  • 2009.1    

    熊本大学理学部非常勤講師

  • 2008.11    

    千葉大学理学部非常勤講師

  • 2004.4 - 2007.3

    一橋大学大学院商学研究科助教授

  • 2007.2    

    信州大学理学部非常勤講師

  • 2006.11    

    千葉大学理学部非常勤講師

  • 2006.7    

    広島大学大学院理学研究科非常勤講師

  • 2005.11    

    筑波大学大学院数理物質科学研究科非常勤講師

  • 2005.5 - 2005.6

    東北大学理学部非常勤講師

  • 2004.11    

    千葉大学理学部非常勤講師

  • 2000.4 - 2004.3

    一橋大学大学院商学研究科講師

  • 2002.11    

    名古屋大学大学院多元数理科学研究科非常勤講師

  • 2000.11    

    東京都立大学理学部非常勤講師

  • 1998.10 - 2000.3

    一橋大学商学部講師

  • 1995.4 - 1998.9

    東京工業大学理学部助手

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Professional Memberships

  • 2003.4 - Now

    日本金融・証券計量・工学学会(JAFEE)

  • 1998.11 - Now

    日本数学会

  •   - Now

    日本応用数理学会

  • 数理経済学会

  • 日本ファイナンス学会

  • 日本保険・年金リスク学会(JARIP)

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Research Interests

  • Probability Theory

  • Martingales

  • Mathematical Finance

Research Areas

  • Natural Science / Mathematical analysis  / Mathematical analysis

Papers

  • A Generalized Cramer-Lundberg Model Driven by Mixed Poisson Processes and Its Ruin Probability

    Masashi Tomita, Koichiro Takaoka, Motokazu Ishizaka

    Chuo Business Review   ( 42 )   19 - 30   2023.2

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    Language:Japanese   Publishing type:Research paper (bulletin of university, research institution)  

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  • On the ruin probability of a generalized Cramer-Lundberg model driven by mixed Poisson processes Reviewed

    Masashi Tomita, Koichiro Takaoka, Motokazu Ishizaka

    Journal of Applied Probability   59 ( 3 )   849 - 850   2022.9

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Cambridge University Press  

    DOI: 10.1017/jpr.2021.99

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  • On a determination formula for the estimation of copula-based Value at Risk Reviewed

    A. M. M. Barreto, N. Ishimura, K. Takaoka

    Proceedings of the 53rd International Symposium on Stochastic Systems Theory and Its Applications   86 - 92   2022.4

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  • Liquidity Shortage and Credit Risk - a Note on the Structural Approach to the Risk of Liquidity Default

    Koichiro Takaoka

    小川英治編著『世界金融危機と金利・為替-通貨・金融への影響と評価手法の再構築』東京大学出版会   169 - 179   2015.3

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  • Optimal Risk Sharing in the Presence of Moral Hazard under Market Risk and Jump Risk (jointly worked) Reviewed

    Takashi Misumi, Hisashi Nakamura, Koichiro Takaoka

    Japanese Journal of Monetary and Financial Economics   2   59 - 73   2014.3

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  • A Continuous-Time Optimal Insurance Design with Costly Monitoring Reviewed

    Hisashi Nakamura, Koichiro Takaoka

    Asia-Pacific Financial Markets   21 ( 3 )   237 - 261   2014

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Springer New York LLC  

    We provide a theoretical and numerical framework to study optimal insurance design under asymmetric information. We consider a continuous-time model where neither the efforts nor the outcome of an insured firm are observable to an insurer. The insured may then cause two interconnected information problems: moral hazard and fraudulent claims. We show that, when costly monitoring is available, an optimal insurance contract distinguishes the one problem from the other. Furthermore, if the insured's downward-risk aversion is weak and if the participation constraint is not too tight, then a higher level of the monitoring technology can mitigate both problems. © 2014 Springer Japan.

    DOI: 10.1007/s10690-014-9184-9

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  • A note on the condition of no unbounded profit with bounded risk Reviewed

    Koichiro Takaoka, Martin Schweizer

    Finance and Stochastics   18 ( 2 )   393 - 405   2014

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Springer Verlag  

    As a corollary to Delbaen and Schachermayer's fundamental theorem of asset pricing (Delbaen in Math. Ann. 300:463-520, 1994
    Stoch. Stoch. Rep. 53:213-226, 1995
    Math. Ann. 312:215-250, 1998), we prove, in a general finite-dimensional semimartingale setting, that the no unbounded profit with bounded risk (NUPBR) condition is equivalent to the existence of a strict sigma-martingale density. This generalizes the continuous-path result of Choulli and Stricker (Séminaire de Probabil-ités XXX, pp. 12-23, 1996) to the càdlàg case and extends the recent one-dimensional result of Kardaras (Finance and Stochastics 16:651-667, 2012) to the multidimen-sional case. It also refines partially the second main result of Karatzas and Kardaras (Finance Stoch. 11:447-493, 2007) concerning the existence of an equivalent supermartingale deflator. The proof uses the technique of numéraire change. © Springer-Verlag Berlin Heidelberg 2014.

    DOI: 10.1007/s00780-014-0229-8

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  • The Instantaneous Volatility and the Implied Volatility Surface for a Generalized Black-Scholes Model Reviewed

    Koichiro Takaoka, Hidenori Futami

    Asia-Pacific Financial Markets   17 ( 4 )   391 - 436   2010.12

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    Language:English   Publishing type:Research paper (scientific journal)  

    Takaoka (Asia-Pacific Financial Markets 11:431-444, 2004) proposed a generalization of the Black-Scholes stock price model by taking a weighted average of geometric Brownian motions of different variance parameters. The model can be classified as a local volatility model, though its local volatility function is not explicitly given. In the present paper, we prove some properties concerning the instantaneous volatility process, the implied volatility curve, and the local volatility function of the generalized model. Some numerical computations are also carried out to confirm our results. © 2009 Springer Science+Business Media, LLC.

    DOI: 10.1007/s10690-009-9112-6

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  • デフォルト確率の推定における景気変動の影響とパネル・ロジット・モデルの有用性 (共著)

    松本理, 高岡浩一郎

    『設立10周年記念懸賞論文』㈱金融工学研究所   19 - 61   2010.2

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  • A Note on the Fundamental Theorem of Asset Pricing

    Koichiro Takaoka

    The Hitotsubashi Review   133 ( 3 )   221 - 229   2005.3

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    Language:Japanese   Publishing type:Research paper (bulletin of university, research institution)  

    DOI: 10.15057/15347

    CiNii Books

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  • A complete-market generalization of the Black-Scholes model Reviewed

    Koichiro Takaoka

    Asia-Pacific Financial Markets   11 ( 4 )   431 - 444   2004.12

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    Language:English   Publishing type:Research paper (scientific journal)  

    The author proposes a new single-stock generalization of the Black-Scholes model. The stock price process is Markovian, the volatility is time-varying, and the market is complete. We also consider the option pricing based on our model and a connection with the equilibrium theory. © Springer 2006.

    DOI: 10.1007/s10690-006-9021-x

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  • On the pricing of defaultable bonds using the framework of barrier options Reviewed

    Motokazu Ishizaka, Koichiro Takaoka

    Asia-Pacific Financial Markets   10 ( 2-3 )   151 - 162   2003.9

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    Language:English   Publishing type:Research paper (scientific journal)  

    In the framework of the structural approach of bond pricing, we extend the Fujita-Ishizaka model by considering more realistic payoffs. The payoff to the bondholder at time of default, provided that default occurs prior to maturity, depends on the firm value at time of default. We also find the new measure with the advantage to calculate the value of bond and its financial interpretation. In addition, we present some numerical exmaples. © Springer 2005.

    DOI: 10.1007/s10690-005-6008-y

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  • An extension of the Black-Scholes stock price model

    Koichiro Takaoka

    『新世紀の先物市場』一橋大学大学院商学研究科編,東洋経済新報社   47 - 54   2002.10

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  • An equilibrium model of the short-term stock price behavior

    Koichiro Takaoka

    数理解析研究所講究録   1215   143 - 157   2001.6

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Kyoto University  

    The author proposes a new equilibrium model for stock price processes. We first consider our one-period formulation, and then its continuous-time analogue. The dynamics of the resulting price process is determined by the distribution of risk tolerance among the agents, and for some special case we recover the Black-Scholes stock price model.

    CiNii Books

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  • Is a Fair Gambling Eternally Fair ?

    Koichiro Takaoka

    The Hitotsubashi Review   124 ( 3 )   437 - 446   2000.9

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    Language:Japanese   Publishing type:Research paper (bulletin of university, research institution)  

    DOI: 10.15057/10480

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  • Enigma of Probability

    Koichiro Takaoka

    The Hitotsubashi Review   121 ( 4 )   613 - 624   1999.4

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    DOI: 10.15057/11873

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  • Some remarks on the uniform integrability of continuous martingales Reviewed

    K Takaoka

    SEMINAIRE DE PROBABILITES XXXIII   1709   327 - 333   1999

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER-VERLAG BERLIN  

    In this article we show a property on the tails of the supremum and the quadratic variation of real-valued continuous (local) martingales, and furthermore use the property to give a characterization of uniform integrable martingales. Our result refines or generalizes the main theorems of the following three papers: Az{\'e}ma-Gundy-Yor (1980), Elworthy-Li-Yor (1997), and the continuous martingale version of Galtchouk-Novikov (1997). The present article is also closely related to a recent paper of Elworthy-Li-Yor.

    Web of Science

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  • On the martingales obtained by an extension due to Saisho, Tanemura and Yor of Pitman's theorem Reviewed

    Koichiro Takaoka

    Seminaire de Probabilites XXXI, Lecture Notes in Mathematics 1665, edited by J. Azéma, M. Emery and M. Yor, Springer   256 - 265   1997.6

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  • On the Sparre Andersen transformation for multidimensional Brownian bridge (jointly worked) Reviewed

    Shigeo Kusuoka, Koichiro Takaoka

    Journal of Mathematical Sciences, The University of Tokyo   4 ( 1 )   211 - 227   1997.4

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:The University of Tokyo  

    A family of law-preserving path transformations of $d$-dimensional Brownian bridge (pinned Brownian motion), $d\geq1,$ is constructed. This generalizes a result of one-dimensional cases obtained first by Embrechts, Rogers and Yor. Our approach and theirs are, however, completely different from each other.

    CiNii Books

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  • A class of path transformations of one-dimensional Brownian motion Reviewed

    Koichiro Takaoka

    Stochastic Analysis: Random Fields and Measure-Valued Processes, Israel Mathematical Conference Proceedings(IMCP) Volume 10, edited by J.-P. Fouque K. J. Hochberg and E. Merzbach, published by American Mathematical Society   193 - 201   1996.12

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    The author constructs a class of path transformations of one-dimensional Brownian motion for each of which the resulting process is again a Brownian motion. The proof is obtained by taking the limit of a combinatorial argument of random walks.

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Books

  • 『穴埋め式確率・統計らくらくワークブック』 (共著)

    藤田岳彦, 高岡浩一郎( Role: Joint author)

    講談社  2003.10  ( ISBN:9784061539945

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    Responsible for pages:1~174   Language:Japanese   Book type:Scholarly book

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  • 翻訳:『デリバティブ価格理論入門――金融工学への確率解析』 原著は M. Baxter & A. Rennie, "Financial Calculus" Cambridge University Press

    藤田岳彦氏, 塩谷匡介氏との共訳( Role: Joint author)

    シグマベイスキャピタル社  2001.2  ( ISBN:9784916106513

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    Responsible for pages:1~310   Language:Japanese   Book type:Scholarly book

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Presentations

  • 数理ファイナンスの第 1 基本定理 ―確率積分とマルチンゲール測度― Invited

    高岡 浩一郎

    日本数学会2018年度年会(統計数学分科会)  ( 東京大学駒場キャンパス )   2018.3 

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  • Some Results on the Yard-Sale Model of Asset Exchange

    高岡 浩一郎

    大阪大学確率論セミナー  ( 大阪大学理学部 )   2017.1 

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  • 流動性の不足と信用リスクの分析―流動性デフォルトリスクの構造型アプローチに関する一考察 International conference

    高岡 浩一郎

    第五回吉林大学・一橋大学共同学術フォーラム「グローバル金融危機以降の通貨、銀行及び金融監督」  ( 吉林大学経済学院 )   2016.9  吉林大学経済学院、吉林大学中日経済共同研究センター、一橋大学

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  • 流動性の不足と信用リスクの分析

    高岡 浩一郎

    平成28年度第1回一橋大学政策フォーラム「世界金融危機と金利・為替」  ( 学術総合センター )   2016.7 

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  • 数理ファイナンスの基本定理について

    高岡 浩一郎

    法政大学 浦谷・安田研究室セミナー  ( 法政大学小金井キャンパス )   2015.4 

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  • 数理ファイナンスの基本定理について Invited

    高岡 浩一郎

    金融工学・数理計量ファイナンスの諸問題 2014  ( 大阪大学中之島センター )   2014.12 

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  • 構造型アプローチの Leland モデルに関する一考察

    高岡 浩一郎

    JAFEE信用リスク理論研究部会  ( 学術総合センター )   2012.2 

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  • 数理ファイナンスの基本定理について

    高岡 浩一郎

    一橋大学数理科学セミナー  ( 一橋大学第3研究館 )   2012.1 

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  • 数理ファイナンスの基本定理について

    高岡 浩一郎

    関西大学確率論セミナー  ( 関西大学第四学舎二号館 )   2011.10 

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  • 信用リスクの構造型モデルに関する一考察

    高岡 浩一郎

    金融工学教育センター (cfee) 研究発表会  ( 一橋大学大学マーキュリータワー )   2011.10 

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  • NUPBR (no unbounded profit with bounded risk) 条件とstrict martingale density の存在との同値性

    高岡 浩一郎

    数理ファイナンスとその周辺  ( 東京大学(本郷キャンパス)小島ホール2階コンファレンスルーム )   2011.1 

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  • On the Condition of No Unbounded Profit with Bounded Risk International conference

    高岡 浩一郎

    Workshop on Mathematical Finance and Related Issues  ( 京都リサーチパーク )   2010.9 

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  • On the Condition of No Unbounded Profit with Bounded Risk International conference

    高岡 浩一郎

    Topics in Mathematical Finance II  ( 大阪大学基礎工学研究科I棟204 )   2010.8 

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  • NUPBR (no unbounded profit with bounded risk) 条件とstrict martingale density の存在との同値性

    高岡 浩一郎

    数理ファイナンス水曜セミナー  ( 東京大学数理科学研究科(駒場) )   2010.6 

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  • Black-Scholes モデルの拡張について

    高岡 浩一郎

    首都大学数理解析セミナー  ( 首都大学8号館 )   2009.10 

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  • On a complete-market generalization of the Black-Scholes model International conference

    高岡 浩一郎

    Mathematical Finance and Related Topics in Economics and Engineering  ( 関西セミナーハウス(京都市) )   2009.8 

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  • Black-Scholes モデルの拡張について

    高岡 浩一郎

    京都大学数学科談話会  ( 京都大学理学研究科数学科 )   2009.7 

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  • The instantaneous volatility and the implied volatility surface for a generalized Black-Scholes model

    高岡 浩一郎, 二見 英徳

    中之島ワークショップ「金融工学・数理計量ファイナンスの諸問題 2008」  ( 大阪大学中之島センター7階セミナー室 )   2008.12 

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  • ある拡張型 Black-Scholes モデルの瞬間的ボラティリティ過程について

    高岡 浩一郎

    中之島ワークショップ「金融工学・数理計量ファイナンスの諸問題 2009」  ( 大阪大学中之島センター7階 )   2008.12 

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  • The instantaneous volatility and the implied volatility surface for a generalized Black-Scholes model

    高岡 浩一郎, 二見 英徳

    The 8th Ritsumeikan International Symposium on Stochastic Processes and Application to Mathematical Finance and the 8th Columbia-Jafee Conference on Mathematical Finance  ( キャンパスプラザ京都 )   2008.3 

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  • The instantaneous volatility and the implied volatility surface for a generalized Black-Scholes model

    高岡 浩一郎, 二見 英徳

    JAFEE(日本金融・証券計量・工学学会)2007年度冬季大会  ( 中央大学駿河台記念館(東京都千代田区) )   2007.12 

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  • Black-Scholes モデルの拡張について

    高岡 浩一郎

    解析セミナー  ( 立命館大学 数理科学科(ウエストウイング7階 数学第3研究室) )   2007.11 

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  • A complete-market generalization of the Black-Scholes model Invited

    高岡 浩一郎

    2006年度JAFEE賞授与式  ( 筑波大学東京キャンパスG501 )   2007.4 

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  • A complete-market generalization of the Black-Scholes model International conference

    高岡 浩一郎

    The Fourth World Congress of the Bachelier Finance Society  ( 一橋大学大学院国際企業戦略研究科(東京都千代田区) )   2006.8 

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  • A complete-market generalization of the Black-Scholes model

    高岡 浩一郎

    数理ファイナンス水曜セミナー  ( 東京大学数理科学研究科118号室(駒場) )   2006.7 

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  • Black-Scholes モデルの拡張について

    高岡 浩一郎

    広島確率論・力学系セミナー  ( 広島大学大学院理学研究科B701号室(鏡山キャンパス) )   2006.7 

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  • 数理ファイナンスの基本定理について

    高岡 浩一郎

    九州確率論セミナー  ( 九州大学理学部3号館 3110 号室 )   2005.2 

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  • 数理ファイナンスの基本定理について

    高岡 浩一郎

    東京確率論月曜セミナー  ( 東京工業大学(大岡山)本館3階34号室 )   2005.1 

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  • 数理ファイナンスの基本定理について

    高岡 浩一郎

    解析セミナー  ( 立命館大学 数理科学科 )   2005.1 

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  • 数理ファイナンスの第1基本定理と structure condition

    高岡 浩一郎

    数理ファイナンス水曜セミナー  ( 東京大学数理科学研究科126号室(駒場) )   2004.11 

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  • マルチンゲールやその stochastic exponential の一様可積分性について

    高岡 浩一郎

    Stochastic Analysis, Stochastic Control and Mathematical Finance  ( 大阪大学基礎工学研究科J棟617 )   2004.2 

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  • Black-Scholes 株価モデルの1つの拡張

    高岡 浩一郎

    第53回理論応用力学講演会  ( 日本学術会議(六本木) )   2004.1 

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  • Black-Scholes 株価モデルの1つの拡張

    高岡 浩一郎

    JAFEE(日本金融・証券計量・工学学会)2003年度冬季大会  ( 学術総合センター一橋記念講堂(東京都千代田区) )   2003.12 

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  • On Kazamaki's criterion for continuous exponential martingales

    高岡 浩一郎

    数理ファイナンス小研究会  ( 大阪大学シグマホール セミナー室1 )   2003.7 

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  • 数理ファイナンスの第1基本定理に関するサーベイおよび補足

    高岡 浩一郎

    数理ファイナンス水曜セミナー  ( 東京大学数理科学研究科126号室(駒場) )   2003.6 

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  • On Kazamaki's criterion for continuous exponential martingales

    高岡 浩一郎

    東京確率論月曜セミナー  ( 東京工業大学(大岡山)本館3階34号室 )   2003.5 

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  • On Kazamaki's criterion for continuous exponential martingales International conference

    Koichiro Takaoka

    l'Ecole d'Ete des Probabilites de St-Flour  ( St-Flour, France )   2002.7 

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  • A remark on Pitman's 2M-X theorem Invited International conference

    Koichiro Takaoka

    Seminaire de Calcul Stochastique  ( ストラスブール大学 )   2002.3 

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  • A generalization of the Black-Scholes stock price model International conference

    Koichiro Takaoka

    Seminaire Mathematiques de l'Economie et de la Finance  ( L'Institut Henri Poincare )   2001.11 

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  • ある種の均衡モデルから導かれる資産価格過程

    高岡 浩一郎

    横浜市立大学理学部数理科学教室談話会  ( 横浜市立大学理学部 )   2001.1 

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  • ある種の均衡モデルから導かれる資産価格過程

    高岡 浩一郎

    経済の数理解析(京都大学数理解析研究所研究集会 研究者代表 丸山徹)  ( 京大会館 101 号室 )   2000.12 

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  • An equilibrium model of the short-term stock price behavior International conference

    Koichiro Takaoka

    Rencontre franco-japonaise de Probabilites  ( パリ第6・7大学 )   2000.11 

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  • ある種の均衡モデルから導かれる資産価格過程

    高岡 浩一郎

    関西確率論セミナー  ( 京都大学理学部数学教室 )   2000.11 

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  • ある種の均衡モデルから導かれる資産価格過程

    高岡 浩一郎

    東京確率論月曜セミナー  ( 東京大学 数理科学研究科棟1階 126 号室 (駒場) )   2000.2 

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  • On a class of path transformations of Brownian motion International conference

    Koichiro Takaoka

    Japan-Russia Symposium on Probablity and Mathematical Statistics  ( 東京 )   1995.7 

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Awards

  • JAFEE Best Paper Award

    2007.4   日本金融・証券計量・工学学会(JAFEE)   JAPAN

Research Projects

  • Restructuring Global Financial Regulation and Crisis Management in the New Phase after the Global Financial Crisis

    Grant number:17H02545  2017.4 - 2020.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)  Hitotsubashi University

    Ogawa Eiji

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    Grant amount: \15340000 ( Direct Cost: \11800000 、 Indirect Cost: \3540000 )

    In this research project, we have made clear how global financial regulation and crisis management have been restructured in the new phase after the Global Financial Crisis, from both macroeconomic and microeconomic viewpoints. Specifically, from the macroeconomic one, we investigated the global market behavior after the Crisis, in particular focusing our attention on the effects of various structural changes in investor sentiment, corporate finance, financial markets, and financial intermediation. On the other hand, from the microeconomic viewpoint, we investigated the effects of the structural changes on the corporate financial behavior. In consequence, we drew some policy implications, by synthesizing the results obtained from the two viewpoints. These results are useful for actual policy conducting. We published them widely in the world through international conferences and academic journals and books.

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  • The Global Financial Crisis and Its Effects on Currencies and Finance: Evaluation Methods Revisited

    Grant number:25285098  2013.4 - 2016.3

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (B)  Hitotsubashi University

    OGAWA Eiji, TAKAOKA Koichiro, NAKAMURA Hisashi, TAKAMIZAWA Hideyuki, KOBAYASHI Kenta, MISUMI Takashi, IKEMORI Toshifumi

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    Grant amount: \17420000 ( Direct Cost: \13400000 、 Indirect Cost: \4020000 )

    Since the recent global financial crisis, it has been a pressing need to develop new models of valuation of interest rates and exchange rates. To fill the need, this research project investigated structural changes of financial systems and monetary/exchange rate policies and explored new valuation methods of asset pricing under financial frictions (such as default, information costs, and behavioral inefficiencies). Moreover, from the research work, we drew political implications of financial markets, financial regulation and monetary/exchange rate policies. We published a book, which collected the research papers produced in this research project, entitled "The Global Financial Crisis and Its Effects on Currencies and Finance: Evaluation Methods Revisited" (In Japanese. University of Tokyo Press, March 2016).

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  • Theory of stochastic analysis and its applications

    Grant number:19204010  2007 - 2010

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (A) 

    MATSUMOTO Hiroyuki, TAKEDA Masayoshi, KUMAGAI Takashi, SHIRAI Tomoyuki, KAISE Hidehiro, YANO Kouji, SUGITA Hiroshi, TANIGUCHI Setsuo, SHIOZAWA Yuuichi, FUNAKI Tadahisa, SHIGEKAWA Ichiro, TANEMURA Hideki, SEKINE Jun, HINO Masanori, TAKAOKA Koichiro, OTOBE Yoshimi, AIDA Shigeki, FUJITA Takahiko, INAHAMA Yuzuru

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    Grant amount: \32500000 ( Direct Cost: \25000000 、 Indirect Cost: \7500000 )

    To account of not only the members but also of the researchers on probability theory in Japan, we held several conferences every year, including two international ones, and made connections on study and joint research. Moreover we invited several foreign researchers and the members of this grant attended conferences outside Japan and visited foreign researchers. Through these activities we contributed some progress on theory of stochastic analysis and on applications to study on questions with origins from statistical physics, study of differential equations, spectra of manifolds, mathematical finance and so on.

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  • Study on the global behavior of solutions for the fluid equation

    Grant number:13640206  2001 - 2002

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)  HITOTSUBASHI UNIVERSITY

    ISHIMURA Naoyuki, TAKAOKA Koichiro, YAMAZAKI Masao, MORIMOTO Hiroko

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    Grant amount: \1000000 ( Direct Cost: \1000000 )

    We have undertaken our research projects mainly on the following two subjects.
    (1) Results are obtained for the analysis on the structure of solutions to the steady state of the Kuramoto-Sivashinsky (KS) equation and/or to the Blasius equation. Both equations are related to the fluid dynamics and have the similar third-order differential operator. By use of the monotonicity, the reduction of the third-order equation into the second-order one is performed. In view of this reduction, the existence of blowing-up solutions for the steady state of the KS equation is proved. These kind of solutions have not been mentioned in the literature so far. Moreover, an elementary existence proof of blowing-up solutions for the Blasius equation is also given, which may shed light on the validity of the Blasius equation itself with regard to the Prandtl boundary layer theory.
    (2) Free boundary problems arise in a wide variety of nonlinear sciences, including one-phase fluid flow problem. Here we are concerned with the pricing of American put option. We present an exact integral formula for the solution.

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  • 確率過程論とその数理ファイナンスへの応用

    1998.4 - 2000.3

    科学研究費助成事業  奨励研究(A) 

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  • Studies on the structure of the lattice of clones consisting of multiple-valued logical functions

    Grant number:10640109  1998 - 1999

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)  Hitotsubashi University

    MACHIDA Hajime, FUJITA Takahiko, YAMADA Hiromochi, IWASAKI Shiro, ISHIMURA Naoyuki, YAMAZAKI Masao

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    Grant amount: \2200000 ( Direct Cost: \2200000 )

    A clone is a set of k-valued logical functions which is closed under composition and contains all the projections. The set of all clones consisting of k-valued logical functions is denoted by LィイD2kィエD2. Whereas the structure of LィイD22ィエD2 is completely determined, our knowledge about the structure of LィイD2kィエD2 for k > 2 at present is very little. The main objective of this research is to clarify the structure of LィイD2kィエD2 and we have obtained the following results.
    1. The structure of LィイD23ィエD2 as a metric space
    We have introduced a metric into the lattice LィイD2kィエD2 of clones and showed that LィイD2kィエD2 is a compact metric space. Moreover, we constructed continuous mappings, based on the meet operation, from LィイD23ィエD2 onto LィイD22ィエD2 and studied the images of maximal clones in LィイD23ィエD2 and those of some clones being accumulation points under such mappings.
    2. Minimal clones in LィイD2kィエD2 and related topics
    Since the classification of minimal clones is far from complete, the study of various properties of minimal clones are very important. We have studied a particular problem concerning minimal clones: Given a pair (CィイD21ィエD2, CィイD22ィエD2) of minimal clones, we call it gigantic pair if the union CィイD21ィエD2∪CィイD22ィエD2 generates the whole set of functions. We proved a characterization theorem of gigantic pairs and showed that gigantic pairs exist for most k's.
    3. Study of hyperclones
    Recently, I. G. Rosenberg initiated the study of hyperclones. We continued his work and proved the following: The cardinality of the lattice of all hyperclones on the set {0,1} is of continuum. This is interesting as the cardinality of the lattice of all (ordinary) clones on {0, 1} is countable.
    4. Study of partial clones consisting of partial functions
    We investigated the following problems on partial clones : (1) The minimal number of maximal partial clones whose meet is the trivial partial clone. (2) The minimal number of minimal partial clones whose join is the clone of all partial operations. This is a joint work with Professors L. Haddad and I.G. Rosenberg.

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  • Mathematical Analysis of Infinite Dimensional Stochastic Models

    Grant number:09640246  1997 - 1998

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)  TOKYO INSTITUTE OF TECHNOLOGY

    SHIGA Tokuzo, TANIGUCHI Masaharu, TAKAOKA Koichiro, NINOMIYA Hirokazu, MORITA Takehiko, UCHIYAMA Kohei

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    Grant amount: \3000000 ( Direct Cost: \3000000 )

    Performing the reseach based on the project plan we obtained the following reseach results.
    1. Fleming-Viot processes play an important role in population genetics, for which we obtained two significant results.
    First, we considered the model with mutation and unbounded selectionas genetic factors. In this case it has not proved even the well-posedness of the diffusion processes, which we settled together with the uniqueness problem of the stationary distributions. This work was caried out jointly with S.N.Ethier (USA). Furthermore we solved the problem of diffusion approximation from discrete time Markov chain models.
    Second, we solved a reversibility problem for the Fleming-Viot processes with mutation and selection, that is to characterize the mutation operator for the process to have a reversible distribution. This work was done with Z.H.Li (China) and L.Yau (USA). (Shiga)
    2. We considered a suvival probability problem of random walker in temporarily and spatially varing random environment, and obtained a precise asymprotics of the suvival probability for small parameter rigion. To prove it we developed a detailed analysis of linear stochastic partial differential equations which are dual objects of the random walk model. This result appeared as ajoint work with T.Furuoya.
    Directed polymer model is a closely related with this problem in mathematical context, and we get some significant results on asymptotical behaviorof the random partition function in low dimensional case, which is harder than higher dimensional case. (Shiga)
    3. For a mechanical many particle system Uchiyama established the hydrodynamic limit and identified its hydrodynamic equation, that is a diffusion equation in this situation.
    4. For a dynamical system in cofinite Fuchsian groups which can be regarded as a Markov system, Morita developed a perterbational analysis of the transfer operator and solved some ergodic problem that is related to number theory.
    5. Motivated by mathematical finance Takaoka obtained a neccesary and suffucient condition for a continuous local martingale to be uniformly integrable.

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  • 数理物理・数理生物のモデルに関する確率解析

    Grant number:08454037  1996    

    日本学術振興会  科学研究費助成事業  基盤研究(B)  東京工業大学

    志賀 徳造, 志賀 啓成, 高岡 浩一郎, 二宮 広和, 村田 実, 内山 耕平

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    Grant amount: \4500000 ( Direct Cost: \4500000 )

    研究実施計画に基づいて研究を推進し以下で述べる成果を得た。
    1)相互作用のある拡散系は、統計物理や数理生物の多くの興味深いモデルを含み、その確率解析は無限次元拡散過程の研究にも重要な意味をもつ。その観点から従来、定常分布が多様に存在する状況下でのエルゴード的挙動を研究してきたが、今回は定常分布が自明な場合または存在しない場合のエルゴード的挙動の研究に取り組み、有限系からの近似におけるエルゴード的挙動に関する新しい結果を得た。(Cox-Greven-志賀)
    また、相互作用のある拡散系と一般化された逆正弦法則の問題との関連も明らかになりつつあり、論文として準備中である。(志賀)
    2)無限次元線型マルコフ系の新しいクラスを導入し、対応する標本リアプノフ指数の定義可能性の証明およびカップリング径数に関する漸近挙動を調べ、径数が小さい領域では有限系、無限系ともに同一のオーダーをもつことを証明した。(古尾谷-志賀) このアイディアはランダム環境中のランダムウォークの生存確率の漸近解析に適用可能であり、その結果は論文として掲載予定である。(志賀)
    3)ランダムウォークおよびブラウン運動について種々の観点から研究を進め、2次元ランダムウォークのポテンシャル核の精密な漸近解析(深井-内山)、さらに時空的観点からのウィーナーテストの問題を解決した。(深井-内山) また、ブラウン運動が導く道空間上のある種の保測変換と数々のブラウン汎関数の同分布性との関連を解明した。(高岡)
    4)線型拡散方程式に対する混合問題の非負解の一意性が成り立つための領域の形に関する必要十分条件を与えた。(村田)また、常微分方程式系とそれに拡散項を付けた非線形拡散方程式を解の爆発問題の観点から研究し、常微分方程式系のあらゆる解は原点に収束するのに,その常微分方程式系に拡散を付けた方程式の解は爆発するという興味深い例を見つけた。(二宮)

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  • 無限次元拡散モデルの解析

    Grant number:07640283  1995    

    日本学術振興会  科学研究費助成事業  一般研究(C)  東京工業大学

    志賀 徳造, 高岡 浩一郎, 二宮 広和, 村田 実, 内山 耕平

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    Grant amount: \2500000 ( Direct Cost: \2500000 )

    交付申請書に記載した研究実施計画に基づいて研究を推進し以下で述べる成果を得た。
    1)相互作用のある拡散系は、無限次元拡散モデルの重要なクラスであり、統計物理や数理生物の多くの興味深いモデルを含んでいる。その拡散系でとくに拡散係数が一般の関数の場合には、定常分布の完全な記述を与えるという定常分布問題は重要かつ未解決である。基礎の空間が立方格子の場合で相互作用が均質的かつ拡散係数が有界のときには、この問題はすでに志賀が解決したが、拡散係数が非有界の場合には一般に前者とは異なる現象が現われることを新たに指摘し、各成分が非負かつ相互作用が不偏ならば定常分布はすべて空間的に均質的であることを証明した。
    2)無限次元モデルのエルゴード的挙動を、近似する有限次元モデルから観測する問題に取り組んだ。相互作用が推移的ならば、有限次元モデルから適当な時空スケーリングにより無限系の定常状態のパラメータの揺動を観測できることを相当程度に確立できた。さらに相互作用が再帰的の場合にも2次元では集団平均過程のスケーリング極限の存在を証明した。(T.Cox, A.Grevenとの共同研究として発表予定。)
    3)無限次元線型マルコフ系の新しいクラスを導入し、対応する標本リアプノフ指数の定義可能性を証明した。さらに標本リアプノフ指数のカップリング径数に関する漸近挙動を調べ、これについては有限系、無限系ともに同一のオーダーをもつことを証明した。(この結果は古尾谷祐との共同論文として現在まとめている。)
    4)多粒子のマルコフ力学系に対する流体力学極限の問題はすでに多くの研究がある。それに対し内山は今回、ある古典力学に従う多粒子系の流体力学極限を調べマクロな運動を支配する非線形拡散方程式の導入に成功した。
    5)線型拡散方程式の正値解の一意性問題や競争的非線型拡散方程式などでも村田、二宮により重要な成果を挙げることが出来た。

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Allotted class

  • 2023   基礎数学   Department

  • 2023   数学入門   Department

  • 2023   演習Ⅰ   Department

  • 2023   演習Ⅱ   Department

  • 2023   演習Ⅲ   Department

  • 2023   演習Ⅳ   Department

  • 2023   演習論文   Department

  • 2023   確率論   Department

  • 2023   解析学   Department

  • 2023   課題演習Ⅰ   Department

  • 2023   課題演習Ⅱ   Department

  • 2023   基礎セミナー(経済学)   Graduate school

  • 2023   数理ファイナンスⅠ   Graduate school

  • 2023   数理ファイナンスⅡ   Graduate school

  • 2023   演習Ⅰ(数理ファイナンス)   Graduate school

  • 2023   演習Ⅱ(数理ファイナンス)   Graduate school

  • 2023   特殊研究Ⅰ(数理ファイナンス)   Graduate school

  • 2023   特殊研究Ⅱ(数理ファイナンス)   Graduate school

  • 2023   特殊研究Ⅲ(数理ファイナンス)   Graduate school

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