Probabilities of Ruin in Economics and Insurance under Light- and Heavy-tailed Distributions

Abstract

This research is conducted on ruin problems in two fields. First, the ruin or survival of an economic agent over finite and infinite time horizons is explored for a one-good economy. A recursive relation derived for the intractable ruin distribution is used to compute its moments. A new system of Chebyshev inequalities, using an optimal allocation of different orders of moments over different ranges of the initial stock, provide good conservative estimates of the true ruin distribution. The second part of the research is devoted to the study of ruin probabilities in the general renewal model of insurance under both light- and heavy-tailed claim size distributions. Recent results on the dual problem of equilibrium of the Lindley-Spitzer Markov process provide clues to the orders of magnitude of finite time ruin probabilities in insurance. Extensive empirical studies show the disparity between the performances of light and heavy-tailed theoretical asymptotics vis-a-vis actual probabilities in finite time and/or with finite initial assets.