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Analysis of Life Insurance Lapses and Utility-Maximization of Shareholders’ Expected Profit

Dankyi, D. K. (2001). Analysis of Life Insurance Lapses and Utility-Maximization of Shareholders’ Expected Profit. (Unpublished Doctoral thesis, City, University of London)


The problem of experiencing early terminations of life insurance contract has greatly affected insurers and yet, is one of the areas in the actuarial literature in which has received little attention. As a result of this, insurers guarantee a high yield, and sometimes offer high payouts (surrender and maturity values) in order to avoid surrenders. This makes the pricing of insurance contracts and also, the management of the corresponding asset portfolio difficult. Therefore, we have proposed methods or techniques to minimise the impact of surrenders on the life insurance company’s fund. Particularly, we have looked at the impact of lapses on the performance (leading to profit/loss) of life insurance funds- a profit/loss model has been developed to be used by actuaries to determine the cost of the surrender option arising from the effects of financial and non-financial adverse selection in this regard. As a result, we have proposed techniques that will involve the policyholder in sharing the cost of surrender due to the option available to him, usually, at times which are favourable to him.

Further, numerical optimization routines and stochastic simulation techniques have been used to determine optimal strategic decisions that maximize the expected shareholders’ profit. It links the approaches of utility theory and mean-variance analysis in obtaining numerical solutions (optimal values). In view of the fact that the life office could lose most of its prospective policyholders as a result of charging a higher premium (the proposed strategy), we have introduced a premium penalty model to take care of this effect.

In the case where there is a financial incentive to surrender, the optimal strategy is to impose a low premium loading for all values of r, which is different from the market loading and a low surrender penalty. By this strategy, the volume of business is expected to increase and so is the shareholders’ expected profit. However, for the case where there is no financial incentive to surrender, the optimal strategy is to impose a high premium loading, not too close to the assumed market loading and charge a higher surrender penalty for relatively risk tolerant investors (for r > /2). This was found to increase the corresponding shareholders’ expected profit. Also, the results show that an optimal way of regulating the surrender basis is to change the surrender basis whenever the rate of investment return on assets rises by one and half percent or falls by a little above one percent. In view of the fact that the strategic decisions are considered in the context of utility theory, the results of the analysis have been shown to be similar to those of modern portfolio theory, as presented by Markovitz (1952). Finally, we have shown that the use of incorrect strategies can have an important effect on the shareholders’ expected profit.

Publication Type: Thesis (Doctoral)
Subjects: H Social Sciences > HG Finance
Departments: Bayes Business School > Actuarial Science & Insurance
Bayes Business School > Bayes Business School Doctoral Theses
Doctoral Theses
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