Comparison of ruin probability estimates in the presence of heavy tails
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Abstract
Four methods of estimation of the ruin probability in the presence of heavy tails are compared in accordance with their effectiveness on the Pareto-distributed claim sizes. The first method, proposed by Embrechis and Veraverbeke, provides an asymptotic expression when the initial capital tends to infinity. The second method, proposed by Goovaerts and De Vylder, provides an algorithm for two-sided estimation based on the solution of the renewal equation through discretization. Its advantage is the perfect applicbility in cases with small initial capital. The third method, proposed initially by Willmoi and improved by Kalashnikov, provides an upper bound of the ruin probability with the help of a test function. The last method, proposed by Kalashnikov, provides two-sided bounds for the ruin probability using truncation of random variables to avoid the Cramér condition. The last two methods enable one to handle cases with intermediate initial capital.
Keywords
Probability Estimate Asymptotic Expression Heavy Tail Initial Capital Claim SizePreview
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