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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.

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