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

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Presentation on theme: "Mean- Variance Portfolio Selection for a Non- life insurance Company Łukasz Delong, Russell Gerrard Agata Kłeczek, Prague 8.03.2012 1."— Presentation transcript:

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

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

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

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

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

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

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 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

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


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