Optimal investment for insurers when the stock price follows an exponential Lévy process |
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Authors: | Radostina Kostadinova |
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Affiliation: | Graduate Program Applied Algorithmic Mathematics, Munich University of Technology, D-85747 Garching, Germany |
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Abstract: | We consider a stochastic model for the wealth of an insurance company which has the possibility to invest into a risky and a riskless asset under a constant mix strategy. The total claim amount is modeled by a compound Poisson process and the price of the risky asset follows a general exponential Lévy process. We investigate the resulting reserve process and the corresponding discounted net loss process. This opens up a way to measure the risk of a negative outcome of the reserve process in a stationary way. We provide an approximation of the optimal investment strategy which maximizes the expected wealth of the insurance company under a risk constraint on the Value-at-Risk. We conclude with some examples. |
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Keywords: | primary, 60G51, 62P05 secondary, 91B28, 91B30 |
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