Better than pre-committed optimal mean-variance policy in a jump diffusion market

Yun Shi (), Xun Li () and Xiangyu Cui ()
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Yun Shi: Shanghai University
Xun Li: The Hong Kong Polytechnic University
Xiangyu Cui: Shanghai University of Finance and Economics

Mathematical Methods of Operations Research, 2017, vol. 85, issue 3, No 1, 327-347

Abstract: 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.

Keywords: Mean field approach; Pre-committed optimal mean-variance policy; Jump diffusion market; Time consistency in efficiency; Semi-self-financing revised policy (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s00186-017-0572-6

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