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Tail bounds for the distribution of the deficit in the renewal risk model. (English) Zbl 1189.91080
Summary: We obtain upper and lower bounds for the tail of the deficit at ruin in the renewal risk model, which are (i) applicable generally; and (ii) based on reliability classifications. We also derive two-side bounds, in the general case where a function satisfies a defective renewal equation, and we apply them to the renewal model, using the function \(\Lambda_u\) introduced by G. Psarrakos and K. Politis [Stoch. Models 25, No. 1, 90–109 (2009; Zbl 1159.91412)]. Finally, we construct an upper bound for the integrated function \(\int_y^{\infty} \Lambda_u(z)\text dz\) and an asymptotic result when the adjustment coefficient exists.

91B30 Risk theory, insurance (MSC2010)
60K10 Applications of renewal theory (reliability, demand theory, etc.)
62P05 Applications of statistics to actuarial sciences and financial mathematics
Full Text: DOI
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