Heterogeneous Premiums for Homogeneous Risks? Asset Liability Management under Default Probability and Price-Demand Functions

We consider an asset liability model under an internal solvency constraint that includes default probability as well as price-demand functions and combine insights from empirical and theoretical research. Furthermore, as a result of policyholders’ heterogeneous willingness to pay, we introduce heterogeneous premiums to maximize the insurer’s overall net present value and compare the results with an optimal homogeneous premium. To determine a reservation price for the insurer, we use the Margrabe-Fischer option-pricing formula. Our numerical examples document that heterogeneous premiums for homogeneous risks improve the net present value when correct expectations underlie and are vulnerable against a cost shift but do not per se induce a decrease in the net present value. Moreover, we recognize that the optimal price setting under overall net present value maximization varies from the underwriting net present value maximization on the individual risk level. Hence, in practice, an overall asset liability management perspective should be in focus to reach the best results from the company’s point of view.