Research on pricing theory by convex risk measures taking account of hedging, and its related stochastic analysis

考虑套期保值的凸风险测度定价理论及其相关随机分析

• 批准号: 22540149
• 负责人: ARAI Takuji
• 金额: $ 1.66万
• 依托单位: Keio University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010-04-01 至 2013-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540149/
• 关键词: 数理ファイナンス; 価格付け理論; 非完備市場; リスク測度; Orlicz空間; Good deal bound; 効用関数; 同値martingale測度; Orlicz space; Scmimartingale

I have studied convex risk measures on stochastic processes in order to deal with shortfall risk measures for American options. In particular, I introduced spaces of stochastic processes whose maximum belongs to an Orlicz space; and obtained representation results for convex risk measures defined on such spaces. Next, I have researched on relationship between convex risk measures and good deal bounds. Supposing the market is a convex cone, I investigated (1) properties of superhedging cost, (2) the equivalence for a convex risk measure between that it represent upper and lower bounds of a good deal bound and that it is given as a risk indifference price, (3) extensions of the fundamental theorem of asset pricing. In addition, I extended the above results to the case where the market is merely convex.

为了研究美式期权的亏额风险测度，本文研究了随机过程上的凸风险测度。特别是，我介绍了空间的随机过程，其最大值属于Orlicz空间，并获得了表示结果，凸风险措施定义在这样的空间。其次，研究了凸风险测度与良交易界的关系。假设市场是一个凸锥，研究了（1）超套期保值成本的性质，（2）凸风险测度表示好交易上界和下界与风险无差别价格的等价性，（3）资产定价基本定理的推广.此外，我还将上述结果推广到了市场仅仅是凸的情况。

项目成果

Convex risk measures on Orlicz spaces: inf-convolution and shortfall

• DOI: 10.1007/s11579-010-0028-8
• 发表时间: 2010-05
• 期刊: Mathematics and Financial Economics
• 影响因子: 1.6
• 作者: Takuji Arai

ショートフォールリスク測度とその表現

短缺风险度量及其表达

• 发表时间: 2012
• 期刊: 三田学会雑誌
• 作者: 岩本誠一;吉良知文;植野貴之;Yutaka Kimura;Toshio Suzuki (with M. Kumabe);Takayuki Ueno;Toshio Suzuki;Yutaka Kimura;新井拓児
• 通讯作者: 新井拓児

How much can investors discount

投资者可以折价多少

• DOI: 10.1007/978-4-431-53883-7_1
• 发表时间: 2011
• 作者: Takuji Arai;Takamasa Suzuki
• 通讯作者: Takamasa Suzuki

CONVEX RISK MEASURES FOR GOOD DEAL BOUNDS

• DOI: 10.1111/mafi.12020
• 发表时间: 2011-08
• 期刊: Mathematical Finance
• 影响因子: 1.6
• 作者: Takuji Arai;M. Fukasawa

Convex risk measures for cadlag processes on Orlicz spaces

Orlicz 空间上的 cadlag 过程的凸风险度量

• 作者: 宮原 孝夫;Yoshio Miyahara and Yoshiki Tsujii;Takuji Arai;新井拓児
• 通讯作者: 新井拓児