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Portfolio Optimization

Published online by Cambridge University Press:  29 August 2014

René Schnieper
René Schnieper*
Affiliation:
Zurich Insurance Company, Reinsurance
*
Zurich Insurance Company, Reinsurance P.O. Box, CH - 8022 Zurich, Switzerland
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Abstract

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Based on the profit and loss account of an insurance company we derive a probabilistic model for the financial result of the company, thereby both assets and liabilities are marked to market. We thus focus on the economic value of the company.

We first analyse the underwriting risk of the company. The maximization of the risk return ratio of the company is derived as optimality criterion. It is shown how the risk return ratio of heterogeneous portfolios or of catastrophe exposed portfolios can be dramatically improved through reinsurance. The improvement of the risk return ratio through portfolio diversification is also analysed.

In section 3 of the paper we analyse the loss reserve risk of the company. It is shown that this risk consists of a loss reserve development risk and of a yield curve risk which stems from the discounting of the loss reserves. This latter risk can be fully hedged through asset liability matching.

In section 4 we derive our general model. The portfolio of the company consists of a portfolio of insurance risks and of a portfolio of financial risks. Our model allows for a simultaneous optimization of both portfolios of risks. A theorem is derived which gives the optimal retention policy of the company together with its optimal asset allocation.

Some of the material presented in this paper is taken from Schnieper, 1997. It has been repeated here in order to make this article self contained.

Keywords

Reinsuranceretentionsnon linear optimizationinsurance riskfinancial riskMarkowitz's portfolio selection methodCAPM
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 30 , Issue 1 , May 2000 , pp. 195 - 248
Copyright
Copyright © International Actuarial Association 2000

References

Houthakker, H.S. and Williamson, P.J. (1996) The Economics of Financial Markets. Oxford University Press.CrossRefGoogle Scholar
Mayers, D. and Smith, C.W. Jr. (1982) On the Corporate Demand for Insurance. Journal of Business, Vol. 55, no. 2.Google Scholar
Panjer, H.H.et al. (1998) Financial Economics. The Actuarial Foundation.Google Scholar
Schnieper, R. (1997) Capital Allocation and Solvency Testing. SCOR Notes.Google Scholar
Sharpe, W.F. (1970) Portfolio Theory and Capital Markets. McGraw-Hill.Google Scholar