Estimation of ruin probabilities

Consider the compound Poisson claim size process generated by a distribution function B. Denote by W(t. x) the finite time non-ruin probability that the company will not be ruined before 1 starting with initial reserve x. Under appropriate conditions on B it is shown that W(t, χ)−W(∞, χ) is basically of the form exp{−θt−υχ}⋯t 32⋯χ for large t, where θ and υ are positive constants.

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