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Approximations for moments of deficit at ruin with exponential and subexponential claims. (English) Zbl 1092.62599
Summary: Consider a renewal insurance risk model with initial surplus $$u>0$$ and let $$A_u$$ denote the deficit at the time of ruin. This paper investigates the asymptotic behavior of the moments of $$A_u$$ as $$u$$ tends to infinity. Under the assumption that the claim size is exponentially or subexponentially distributed, we obtain some asymptotic relationships for the $$\phi$$-moments of $$A_u$$, where $$\phi$$ is a non-negative and non-decreasing function satisfying certain conditions.

##### MSC:
 62P05 Applications of statistics to actuarial sciences and financial mathematics 91B30 Risk theory, insurance (MSC2010) 62E20 Asymptotic distribution theory in statistics
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##### References:
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