A Risk Extended Version of Merton’s Optimal Consumption and Portfolio Selection
将方差作为风险度量引入经典默顿问题，在均值场型控制框架下求解这一时间不一致问题，推导最优性条件并给出数值结果，适用于各类投资或运营决策。
A risk management version of the classical investment-consumption problem known as Merton's problem in the finance literature is proposed. Risk is measured by variance, which introduces a nonlinear function of the expected value into the control problem. Standard stochastic theory cannot properly handle this type of nonlinear stochastic optimization problem. Therefore, we study this time-inconsistent problem within the mean field-type control framework. We derive the sufficient condition of optimality and solve the problem completely. Numerical results illustrating the effect of risk on optimal policies are also presented. Applications can be numerous, including all kinds of investment decisions or operations decisions.