2013 Fiscal Year Final Research Report
New developments of estimations and numerical analysis in finance
| Project/Area Number |
23740089
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Hosei University |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2013
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| Keywords | フィルタリング / フラクショナルブラウン運動 / マリアヴァン解析 / グリークス |
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| Research Abstract |
Three main studies on estimations and numerical analysis in mathematical finance were considered. 1. A convergence rate to the real value of an approximation of the Bayesian estimator with respect to a number of data and choice of approximating parameters were theoretically given. Effects of filtering in expected utility maximization problems were also studied. 2. Using the Malliavin calculus, Greeks, which is one of risk measure, under a financial model with fractional Brownian motions were given and some effects were numerically confirmed. 3. Existence of jumps in Japanese stock markets and estimations of the distribution were studied. Existence of asset bubbles was also studied.
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