Incorporating Foreign Equities in the Optimal Asset Allocation of an Insurer with the Consideration for Background Risks: Models and Numerical Illustrations

We analyzes the optimal asset allocation problem for life insurers that are required to cope with significant background risks originating from life insurance businesses among a set of stochastic investment opportunities including foreign equities. The insurer is assumed to maximize the expected discounted utility of its surplus over a time horizon, and the optimalization problem is formulated in a stochastic control framework. Our derivations show that the optimal portfolio can be characterized by three components: a risk-minimizing component, a risk aversion index coupled with the portfolios performance index, and the component reflecting the diffusions of state variables. Since the explicit solutions cannot be derived due to the complexity of the model, we employ Markov chain approximation methods to obtain the optimal control solutions numerically. The model and numerical methods are then applied to a hypothetical insurer in a simplified setting as an illustrative example.