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Abstract
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Researchers in actuarial mathematics have widely applied the indifference principle via expected utility as a premium principle. In short, one calculates the premium that makes the insurer indifferent between not insuring the risk and insuring the risk for the given premium, in which one measures risk (and thereby indifference) by expected utility. In this paper, we propose using the probability of ruin as the risk measure. Specifically, we calculate the premium that makes the insurer's probability of ruin after insuring a given risk equal to that before insuring the risk. In Part I of this two-part talk, we consider the control of investing in a risky asset to minimize the probability of ruin. In Part II, we consider the additional control of purchasing quota-share reinsurance. We demonstrate our results with a numerical example. This is joint work with S. David Promislow from York University. |
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