Continuous-Time Dynamic Programming for ALM with Risk Averse Loss Functions

In this paper we extend the continuous-time dynamic programming approach for Asset/Liability Management from Boulier et al. (1995). It is an extension in the sense that we consider objective functions for pension fund management that are different from the standard quadratic loss functions. In particular, we calculate optimal policies for a loss function with Constant Relative Risk Aversion (CRRA) as well as one with Constant Absolute Risk Aversion (CARA). Taking these specific loss functions is based on the work of Merton (1990), as he uses these same functions as utility functions for the consumption/investment framework. For each loss function we solve the associated HJB-equation and obtain closed form solutions.