The effect of the nature of the liabilities on the solvency and maturity payouts of a UK life office fund: a stochastic evaluation

Several studies have shown that a simulation model of participating life insurance business must reflect explicitly the major decisions which are left to the discretion of management. In the UK these decisions include asset allocation and bonus distribution. It is also common in the UK to use premium bases which do not explicitly account for the expectation that a terminal bonus will be paid, while using a uniform system of reversionary bonus for business of all terms. Here, we show that this results in short-term business being at much greater risk of insolvency than long-term business, under a variety of investment strategies. Our main purpose is to study the effect of small changes to the parameters of the investment model used on the outcomes described above. For this purpose we compare results using two versions of the Wilkie model (Wilkie, A.D., 1986. A stochastic investment model for actuarial use. Transactions of the Faculty of Actuaries 39, 341–403, Wilkie, A.D., 1995. More on a stochastic asset model for actuarial use. British Actuarial Journal 1, 1–168.) We show that small changes in the variances of the economic series modelled have a marked impact on solvency, while changes in maturity values are mostly the result of a small change in the rate of real dividend growth.