Insolvency risk and its impact on the policyholders' investment choices: a mean-variance approach for participating life insurance business in UK

Ross and McWhirter (Ross and McWhirter, 1991. Unpublished paper) and Berketi and Macdonald (Berketi and Macdonald, 1999. Insurance: Mathematics and Economics 24, 117-138) showed that diversifying insolvency risk results in a substantial cost to the policyholders in terms of reduction in their expected maturity value payouts. The implication is that, contrary to the office's objectives, it may not be worth avoiding insolvency from the policyholder's point of view. In this paper we show that, when risk las measured by the volatility of the final payment) is also taken into account, the policyholder' s and the office's objectives do not necessarily contradict each other. Employing a mean-variance framework to model various investment options we find that the policyholder will still find advantage in investing with the life office, despite the lower final payments it may give, allowing the office to deal with insolvency. It is also shown that a solvency-driven dynamic investment strategy is a less costly and more effective method in dealing with insolvency than the alternative of the asset share charging method as suggested by Needleman and Roff.(Needleman and Roff, 1995. British Actuarial Journal 1 (IV), 603-688.) Finally, we distinguish the operation of participating life insurance from unit-linked business by introducing maturity value smoothing. We mainly concentrate on the effect of the averaging period of smoothing on the volatility of payouts and on the office's solvency. We find that the investors will select for their portfolios only the life offices that offer the highest degree of maturity value smoothing. The effect of the solvency consideration in this framework has as an inevitable result the downward shift of the investor's efficient frontier. (C) 1999 Elsevier Science B.V. All rights reserved.