| Project/Area Number |
23540133
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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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 | Osaka University |
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Principal Investigator |
SEKINE Jun 大阪大学, 基礎工学研究科, 教授 (50314399)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | long term investment / downside risk / floor constraint / drawdown constraint / Wishart factor model / Lugannani RIce formula / 鞍点法 / フロアー制約 / 条件付き線形モデル / 効用最大化 / 効用無差別価格 / 非線形富過程 / BSDE / リスク鋭感的ポートフォリオ最適化 / 長期間双曲的成長率 / Wishart型ファクターモデル / 非完備市場 / 大偏差制御 / 長時間最適化 / 低下制約 / Wishart型自己回帰過程 |
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| Research Abstract |
Long-term optimal investment problems and related large deviation control problems are stutied, and the following results are obtained:(i) For the floor constrained problem, a characterization of optimal solution is presented and the construction methods (in five ways) of optimal solution is provided. (ii) Optimal solution is constructed for the generalized drawdown constrained problem. Moreover, the problem with both floor and drawdown constraint is treated. (iii) As a tractable and computable example, Wishart factor model is presented and studied. (iv) A different approach to large deviation control problem via duality is explored.
Also, a theoretical order estimate is obtained for the Lugannani-Rice formula, which is the approximation formula for the tail probability, based on the saddle-point approximation technique.
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