Effect of Labour Income on the Optimal Bankruptcy Problem

In this paper we deal with the optimal bankruptcy problem for an agent who can optimally allocate her consumption rate, the amount of capital invested in the risky asset as well as her leisure time. In our framework, the agent is endowed by an initial debt, and she is required to repay her debt continuously. Declaring bankruptcy, the debt repayment is exempted at the cost of a wealth shrinkage. We implement the duality method to solve the problem analytically and conduct a sensitivity analysis to the cost and benefit parameters of bankruptcy. Introducing the flexible leisure/working rate, and therefore the labour income, into the bankruptcy model, we investigate its effect on the optimal strategies.