Mean–variance investment and risk control strategies — A time-consistent approach via a forward auxiliary process

We consider an optimal investment and risk control problem for insurer under the mean–variance (MV) criterion. By introducing a deterministic auxiliary process defined forward in time, we formulate alternative time-consistent related to original MV problem, obtain strategy value function new closed-form. compare our formulation those precommitment game-theoretic framework. Numerical studies show that, when financial market is negatively correlated with process, may involve short selling risky asset and, if that happens, less averse sells more asset.