Consider an insurance risk model, in which the surplus process satisfies a recursive equation U n=U n-1 (1+r n)-X n for n≥ 1, where U 0=x≥0 is the initial surplus, {r n;n≥1} the interest rate sequence, {X n;n≥1} the sequence of i.i.d. real-valued random variables with common distribution function F, which denotes the gross loss during the nth year. We investigate the ruin probability within a finite time horizon and give the asymptotic result as x→∞.
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