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

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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

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amounts of successive claims counts the number of claims Agata Kłeczek, Prague

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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

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THE MODEL Financial market Claim process Claim intensity process Agata Kłeczek, Prague

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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

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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

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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

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

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