Optimal consumption-investment and life insurance strategy with market frictions

We consider the optimal investment, consumption and life insurance decision-making problem with market frictions. The policyholder allocates her wealth among a risk-free asset and multiple return-predictable risky assets. Each trade not only incurs a quadratic transaction cost from temporary price impact but also induces a persistent price impact that causes distortion in asset returns. Mortality risk is mitigated through dynamically adjustable life insurance coverage. With these facts incorporated simultaneously, we solve the resulting Hamilton–Jacobi–Bellman (HJB) equation by utilizing the dynamic programming principle and obtain closed-form solution for the optimal strategy and corresponding value function. Furthermore, we provide sufficient conditions for the existence and uniqueness of solution to the induced matrix Riccati differential equation system and prove the verification theorem for the dynamic stochastic optimization problem. While confirming existent observations in the literature, numerical analyses provide valuable guidance for the decisions maker and especially reveal that persistent price impact makes consumption and investment move in the same direction, while temporary price impact makes them move in opposite directions.