4 research outputs found
Derivative-free hybrid methods in global optimization and their applications
In recent years large-scale global optimization (GO) problems have drawn considerable attention. These problems have many applications, in particular in data mining and biochemistry. Numerical methods for GO are often very time consuming and could not be applied for high-dimensional non-convex and / or non-smooth optimization problems. The thesis explores reasons why we need to develop and study new algorithms for solving large-scale GO problems .... The thesis presents several derivative-free hybrid methods for large scale GO problems. These methods do not guarantee the calculation of a global solution; however, results of numerical experiments presented in this thesis demonstrate that they, as a rule, calculate a solution which is a global one or close to it. Their applications to data mining problems and the protein folding problem are demonstrated.Doctor of Philosoph
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Analysis of Life Insurance Lapses and Utility-Maximization of Shareholdersâ Expected Profit
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 companyâs 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 shareholdersâ 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 shareholdersâ 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 shareholdersâ 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 shareholdersâ expected profit