Portfolio Optimization

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 market to market. We thus focus on the economic value of the company. We first analyze 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 analyzed. In section 3 of the paper we analyze the loss reserve risk of the company. It is show 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: Reinsurance, retentions, non linear optimization, insurance risk, financial risk, Markowitz's portfolio selection method, CAPM