In this paper, we propose a model for the optimal premium pricing policy of an insurance company into a competitive environment using Dynamic Programming into a stochastic, discrete-time framework when the company is expected to drop part of the market. In our approach, the volume of business which is related to the past year experience, the average premium of the market, the company's premium which is a control function and a linear stochastic disturbance, have been considered. Consequently, maximizing the total expected linear discounted utility of the wealth over a finite time horizon, the optimal premium strategy is defined analytically and endogenously. Finally, considering two different strategies for the average premium of the market, the optimal premium policy for a company with an expected decreasing volume of business is derived and fully investigated. The results of this paper are further evaluated by using data from the Greek Automobile Insurance Industry.

We have investigated the performance of pension schemes of with-profit policies containing a guaranteed minimum rate of return and we have found that the price of the guarantee measured in terms of lost returns is enormous. We use simple simulations rather than complex pricing methods to illustrate that the price of an interest guarantee is high in pension products that are currently commercialised in the market. We have found that the customer loses up to about 0.75% yearly in the rate of return when an interest guarantee is purchased, compared to the return of an equivalent saving strategy with the same risk at the level 95%. This can explain why such arrangements are not widely popular. Our approach can be used to inform clients, who are not experts in modern financial models, the impact of paying for an interest guarantee.

We study the effects of introducing taxation in classical continuous-time optimization problems with utility from consumption, bequest and retirement savings. Inspired by actual tax favoured retirement savings programs, we formulate and solve the optimization problem for various tax regimes, and compare tax effects on consumption/savings contributions, investment and purchase of life insurance under the regimes. The optimization problems have analytical solutions, which allow for easy comparison of tax effects under the different regimes. To substantiate the results we also present a numerical analysis of the results based on realistic parameter values and regimes. Based on American and Danish tax regimes we estimate the values of existing retirement saving favouring to be 1 – 2 percent of lifetime income.

We analyze the mortality of couples by fitting a multiple state model to a large insurance data set. We find evidence that mortality rates increase after the death of a partner and, in addition, that this phenomenon diminishes over time. This is popularly known as a “broken-heart” effect and we find that it affects widowers more than widows. Remaining lifetimes of joint lives therefore exhibit short-term dependence. We carry out numerical work involving the pricing and valuation of typical contingent assurance contracts and of a joint life and survivor annuity. If insurers ignore dependence, or mis-specify it as long-term dependence, then significant mis-pricing and inappropriate provisioning can result. Detailed numerical results are presented.

This paper synthesizes and extends the literature on multivariate two-part regression modelling, with an emphasis on actuarial applications. To illustrate the modelling, we use data from the US Medical Expenditure Panel Survey to explore expenditures that come in two parts. In the first part, zero expenditures correspond to no payments for health care services during a year. For the second part, a positive expenditure corresponds to the payment amount, a measure of utilization. Expenditures are multivariate, the five components being (i) office-based, (ii) hospital outpatient, (iii) emergency room, (iv) hospital inpatient, and (v) home health expenditures. Not surprisingly, there is a high degree of association among expenditure types and so we utilize models that account for these associations. These models include multivariate binary regressions for the payment type and generalized linear models with Gaussian copulas for payment amounts.

As anticipated, the strong associations among expenditure types allow us to establish significant model differences on an in-sample basis. Despite these strong associations, we find that commonly used statistical measures perform similarly on a held-out validation sample. In contrast, out-of-sample risk measures used by actuaries reveal differences in the association among expenditure types.

A simulation investigation of the effect of default insurance on the optimal equity allocation and deficit spread period of a model defined benefit pension scheme is performed, using the old and new frameworks of the Pension Protection Fund in the U.K. as a starting point. The old default insurance levy framework encourages an increase in the allocation to equities, creating an indirect effect of increased deficits. The new framework reverses the effect to a reduction in the allocation to equities, thus reducing deficits. In addition the gaming element of default insurance is investigated and found to significantly increase optimal equity allocation and deficit spread period, leading to a significant increase in deficits.

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