Purchasing casualty insurance to avoid lifetime ruin

We determine the optimal strategies for purchasing deductible insurance and for investing in a risky financial market in order to minimize the probability of lifetime ruin when an individual is subject to an insurable loss that occurs at a Poisson rate. We specialize to the case for which the casualty loss is constant and insurance is priced actuarially fairly. We learn that the optimal deductible strategy is for the individual to purchase no insurance when her wealth is below a so-called buy level. However, when wealth is greater than the buy level, the individual optimally purchases full insurance coverage.