Optimal Consumption and Investment with Mortality Risk and State Price-Dependent Utilities

We address the problem of optimal consumption and investment for agents with mortality risk in a complete financial market. We achieve the optimization on a functional on the utility of consumption and bequest discounted by the state price process as proposed by Londono [25]. We introduce live insurance˜ to hedge consumers’ mortality risk and to achieve consumers’ optimal consumption in the presence of negative physical wealth. We propose the notion of life insurance completeness that allows for a rich insurance market with agents that can resource to a rich pool of clients with similar mortality structures and allow for hedging. Using a martingale methodology, we develop a full solution under weak conditions for optimal consumption and investment