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

Yun Shi, Xun Li, Xiangyu Cui

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)327-347
Number of pages21
JournalMathematical Methods of Operations Research
Volume85
Issue number3
DOIs
Publication statusPublished - 1 Jun 2017

Keywords

  • Jump diffusion market
  • Mean field approach
  • Pre-committed optimal mean-variance policy
  • Semi-self-financing revised policy
  • Time consistency in efficiency

ASJC Scopus subject areas

  • Software
  • Mathematics(all)
  • Management Science and Operations Research

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