Better Than Pre-Committed Optimal Mean-Variance Policy in a Jump Diffusion Market

20 Pages Posted: 15 Aug 2014

See all articles by Xiangyu Cui

Xiangyu Cui

Shanghai University of Finance and Economics - School of Statistics and Management

Yun Shi

Shanghai University

Xun Li

Hong Kong Polytechnic University

Date Written: August 13, 2014

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 behaviours. 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

JEL Classification: G11

Suggested Citation

Cui, Xiangyu and Shi, Yun and Li, Xun, Better Than Pre-Committed Optimal Mean-Variance Policy in a Jump Diffusion Market (August 13, 2014). Available at SSRN: https://ssrn.com/abstract=2480218 or http://dx.doi.org/10.2139/ssrn.2480218

Xiangyu Cui (Contact Author)

Shanghai University of Finance and Economics - School of Statistics and Management ( email )

777 Guoding Road
Shanghai, Shanghai 200433
China

Yun Shi

Shanghai University ( email )

SHANGDA ROAD 99
Shanghai, SHANGHAI 200444
China

Xun Li

Hong Kong Polytechnic University ( email )

The Hong Kong Polytechnic University
Hung Hom, Kowloon
Hong Kong

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