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