Optimal investment, consumption-leisure, insurance and retirement choice

In this paper, we study an optimal consumption-leisure, investment, insurance and retirement choice problem of an infinitely lived economic agent with constant elasticity of substitution (CES) preferences. We incorporate random insurable losses that are independent of risky asset returns (negative monetary shocks) and impose short-sale constraint on the risky asset to formulate this optimal choice model. When the wealth process is subject to insurable negative monetary shocks produced by a general marked point process, the challenge is to derive an optimal allocation of the agent's wealth between a portfolio investment and an insurance (costly) strategy. Without imposing the level of insurance to be within interval [0,1]; we capture the agent's instantaneous preferences for consumption and leisure via CES preference, while integrating the optimal consumption-leisure-work tradeoffs, the optimal portfolio selection, optimal level of insurance and his/her optimal retirement time. We use the Martingale technique to formulate the optimization problem and solve the optimal policies of the agent by applying the variational inequality arising from the dual functions of the optimal stopping times. Our results demonstrate that a lack of insurance against large negative monetary shocks is positively correlated with lower participation rate in the equity market and high savings rates when short-sale constraint is binding. The optimal retirement time is characterized as the first time when his/her wealth exceeds a critical level of wealth.