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A Stochastic Approach to Find Optimum Reinsurance Arrangements for Life Insurance Companies on the Basis of Maximizing the Utility of Returns

Gonçalves, P. (2000). A Stochastic Approach to Find Optimum Reinsurance Arrangements for Life Insurance Companies on the Basis of Maximizing the Utility of Returns. (Unpublished Doctoral thesis, City, University of London)


The choice of the retention level in life assurance has always been a polemic subject. In most cases, companies will choose the amount that has stand the test of time.

In this project we will determine the optimal retention level that maximizes the utility of returns for a life insurance company. The approach used is to asses the utility of the extra return obtained by the shareholders, by utilizing their capital in support of the life portfolio’s risk as opposed to investing it in a risk free way. The required level of capital is calculated using a ruin probability approach. It is also linked with the exposure to risk, and therefore it allows for lower levels of capital when, through the reinsurance treaty, risk is passed to the reinsurer.

Two approaches were considered. The first, uses an analytical approach and looks at a one-year scenario. The second, looks at a multi-year scenario by using a stochastic approach. Both scenarios look at portfolio of n-year term assurance policies where all policyholders share the same characteristics: age, term of policy, distribution of sum assured, assumptions of the reinsurance treaty, etc.. Variations in the initial set of assumptions are considered and the effect on the optimal retention level analysed.

The results obtained have shown that utility theory can be a way in which capital and reinsurance combinations can be chosen such that shareholders interests are optimized, while ensuring policyholders interests continue to be met. When we were trying to assess the retention level that optimizes expected utility of profits, while still imposing a ruin constraint, we were balancing both policyholders and shareholder's interests. Different optimal retentions and capital levels were obtained as a function of the portfolio characteristics.

Also, we showed possible ways in which parameter risk can be allowed for. We would also note the relative insignificance of process risk compared with parameter risk. The effect of introducing this additional degree of risk (model and/or parameter), on retention level was dramatic. In this, the increase in risk was so dramatic, that even if we were to take into consideration for the trade-off, that must have occurred, both capital and reinsurance needed to be increased. Therefore parameter risk is a much larger component of total risk, having a more significant effect on retention levels.

Publication Type: Thesis (Doctoral)
Subjects: H Social Sciences > HG Finance
Q Science > QA Mathematics
Departments: School of Science & Technology > Mathematics
School of Science & Technology > School of Science & Technology Doctoral Theses
Doctoral Theses
[thumbnail of Goncalves thesis 2000 PDF-A.pdf]
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