Better than pre-committed optimal mean-variance policy in a jump diffusion market |
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Authors: | Yun Shi Xun Li Xiangyu Cui |
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Institution: | 1.School of Management,Shanghai University,Shanghai,China;2.Department of Applied Mathematics,The Hong Kong Polytechnic University,Hong Kong,China;3.School of Statistics and Management, Shanghai Key Laboratory of Financial Information Technology,Shanghai University of Finance and Economics,Shanghai,China |
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Abstract: | Dynamic mean-variance investment model can not be solved by dynamic programming directly due to the nonseparable structure of variance minimization problem. Instead of adopting embedding scheme, Lagrangian duality approach or mean-variance hedging approach, we transfer the model into mean field mean-variance formulation and derive the explicit pre-committed optimal mean-variance policy in a jump diffusion market. Similar to multi-period setting, the pre-committed optimal mean-variance policy is not time consistent in efficiency. When the wealth level of the investor exceeds some pre-given level, following pre-committed optimal mean-variance policy leads to irrational investment behaviors. Thus, we propose a semi-self-financing revised policy, in which the investor is allowed to withdraw partial of his wealth out of the market. And show the revised policy has a better investment performance in the sense of achieving the same mean-variance pair as pre-committed policy and receiving a nonnegative free cash flow stream. |
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