Optimal investment strategy for asset-liability management with a defaultable bond under stochastic default intensity

This paper studies a continuous-time asset-liability management problem with a defaultable bond under stochastic interest rates and stochastic default intensity. Specifically, an asset-liability manager is allowed to invest in a cash, a treasury bond, a defaultable bond and a stock. Using the stochastic control scheme and partial differential equation approach, we derive closed-form expressions for optimal investment strategies and corresponding value functions under the power and exponential utility functions. In addition, we also provide numerical experiments to illustrate the impact of relevant parameters in the default process and recovery rate on the optimal asset allocation strategy.