Ruin probabilities in models of resource management and insurance: A synthesis

This paper synthesizes and contributes to the literature on ruin probabilities in two different contexts. First it explores a Markov (Lindley-Spitzer) process arising in a model of sustainable consumption of a renewable resource under uncertainty. The focus is on the rate of convergence of the stock process, particularly in the heavy-tailed case. Next, it turns to the characterization of the ruin probability in the Sparre Andersen model of insurance. Both the heavy- and light-tailed cases are investigated. Finally, some remarks on the mathematical connections between the two models are made.