This paper deals with the measurement of profitability of a life insurance company from the shareholders' perspective under a Solvency II framework. Profitability and solvency capital requirement of life insurance business are exposed to many levels of uncertainty, in particular with respect to the development of the capital market. Therefore, traditional profitability measures from life insurance are not capable of a deep analysis of modern life insurance business. We propose a method of how modern life insurance business can be analyzed and profitability from the shareholders' perspective can be measured. In our model, shareholders invest in the company by providing capital. This helps the company to maintain a certain level of solvency which is fixed by management rules. We evaluate the stream of cash flows between insurance company and shareholders dependent on the target solvency ratio. The cash flows are of course random as they build upon the stochastic development of the capital market, which we model in terms of stochastic interest rates following a Hull-White model and stocks following a geometric Brownian motion. We study the distribution of the present value of the cash flows as well as the development of the accumulated account of cash flows using risk-adjusted discount factors. Finally, we apply our method to model companies with different types of interest rate guarantees as in [1], [2] and [3]. With a detailed analysis and comparison of the results, we can work out how favorable the products are to shareholders in today's regulatory environment.
[1] Briys, E. and De Varenne, F. (1997), “On the risk of insurance liabilities: Debunking some common pitfalls.” The Journal of Risk and Insurance, vol. 64(4), pp. 673-694.
[2] Grosen, A. and Jørgensen, P.L. (2002), “Life insurance liabilities at market value: An analysis of insolvency risk, bonus policy, and regulatory intervention rules in a barrier option framework.” The Journal of Risk and Insurance, vol. 69(1), pp. 63-91.
[3] Miltersen, K.R. and Persson, S.-A. (2003), “Guaranteed investment contracts: Distributed and undistributed excess return.” Scandinavian Actuarial Journal, vol. 2003(4), pp. 257-279.