2003 Fiscal Year Final Research Report Summary
Applications of Levy Processes to Mathematical Finance
| Project/Area Number |
13640131
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Nagoya City University |
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Principal Investigator |
MIYAHARA Yoshio Nagoya City University, Graduate School of Economics, Professor, 大学院・経済学研究科, 教授 (20106256)
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| Co-Investigator(Kenkyū-buntansha) |
NOTOCHORD Morihiro Nagoya City University, Graduate School of Natural Sciences, Associate Professor, 大学院・システム自然科学研究科, 助教授 (30347421)
SHIMIZU Akinobu Nagoya City University, Graduate School of Natural Sciences, Professor, 大学院・システム自然科学研究科, 教授 (10015547)
MISAWA Tetsuya Nagoya City University, Graduate School of Economics, Professor, 大学院・経済学研究科, 教授 (10190620)
FUJIWARA Tukasa Hyogo University of Teacher Education, Department of Mathematics, Associate Professor, 学校教育学部, 助教授 (30199385)
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| Project Period (FY) |
2001 – 2003
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| Keywords | mathematical finance / option pricing / geometric Levy process / martingale measure / relative entropy |
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| Research Abstract |
We have studied the option pricing problems in the incomplete asset market, which is one of the important problems in the field of mathematical finance. Our goal is the construction of the [Geometric Levy process & MEMM] pricing model, in which the geometric Levy processes are adopted as the underlying asset price processes and the MEMM (=minimal entropy martingale measure) is adopted as the martingale measure. And we have investigated the fundamental theories for the construction of this model and the applications of this mode to the option pricing.
We first established the existence theorem of MEMM for the geometric Levy processes, and we nest investigated the properties of MEMM and the properties of the [Geometric Levy process & MEMM] pricing model. Especially we have studied the relations between the MEMM and the Esscher martingale measure comparing each other. We investigated the methods for the application of this model, for example the method for the estimation of Levy processes. We also investigated the calibration problems of our model.
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