1. Mean- Variance Portfolio Selection for a Non- life insurance Company Łukasz Delong, Russell Gerrard Agata Kłeczek, Prague 8.03.2012 1

2. The insurance risk process collective insurance risk model C(t) denote aggregate claim amount paid up to time t the process is a compound Cox process Agata Kłeczek, Prague 8.03.20122

3. amounts of successive claims counts the number of claims Agata Kłeczek, Prague 8.03.20123

4. The Financial Market Levy diffusion version of a Black- Scholes financial market The price of a risk- free asset is described A risky stock and the dynamics of its price is given by Agata Kłeczek, Prague 8.03.20124

5. THE MODEL Financial market Claim process Claim intensity process Agata Kłeczek, Prague 8.03.20125

6. Problem formulation Portfolio selection for a general insurance company Wealth process of the insurer its dynamics are given by the stochastic differential equation Agata Kłeczek, Prague 8.03.20126

7. Two optimization problems 1)Classical mean-variance portfolio selection. Investment strategy should be chosen in the following way where P is a specified target. Agata Kłeczek, Prague 8.03.20127

8. 2) includes also a running cost penalizing deviations of the insurers wealth from a specified profit-solvency target which is a random process Agata Kłeczek, Prague 8.03.20128

9. Solution of optimization problems Stochastic theory Verification theorem Levy diffusion financial market Agata Kłeczek, Prague 8.03.20129