2016 Fiscal Year Final Research Report
Asymptotic distribution theory for mathematical finance
| Project/Area Number |
24684006
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| Research Category |
Grant-in-Aid for Young Scientists (A)
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| Allocation Type | Partial Multi-year Fund |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Osaka University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2017-03-31
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| Keywords | 数理ファイナンス |
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| Outline of Final Research Achievements |
We extend asymptotic distribution theory of stochastic processes to find explicit solutions to problems in mathematical finance. They include optimal hedging problem under transaction costs, for which we constructed explicit hedging strategies minimizing relative asymptotic hedging error or asymptotic error variance. These results can be seen as developments in approximation theory of stochastic integrals. We studied also small-time asymptotics of stochastic processes which are models for financial asset prices. We derived and validated an asymptotic expansion of marginal distribution to show in particular that models with fractional Brownian motion explain the term structure of option price data.
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| Free Research Field |
確率解析
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