2011 Fiscal Year Final Research Report
Max-plus probabilistic approach to problems related to stochasitic control
| Project/Area Number |
20740052
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Osaka University (2011)
Nagoya University (2008-2010) |
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Principal Investigator |
KAISE Hidehiro 大阪大学, 基礎工学研究科, 准教授 (60377778)
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| Project Period (FY) |
2008 – 2011
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| Keywords | 確率論 / 確率制御 / 動的計画偏微分方程式 / max-plus確率 / 数理ファイナンス |
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| Research Abstract |
Max-plus algebra is obtained by replacing the conventional addition and multiplication with maximum and the addition in reals, respectively. Using max-plus algebra in continuous-time and continuum-state control problems, we obtained new results on structures of solutions and characterizations of value functions for dynamic programming partial differential equations in stochastic and deterministic controls. These results are based on max-plus methodology. We also formulated optimal consumption and investment problems in mathematical finance by max-plus probabilistic point of view and characterized optimal values.
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