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

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.