We give results on the probability of absorption at zero of the diffusion process Xt with X0 = K > 0 and non-Lipschitz diffusion coefficient σx , γ ∈ [ 1 2 , 1): dXt = μXtdt + σX γ t dBt relative to Brownian motion Bt. Our results give information on the time to ruin τ0 = inf{t : Xt = 0}. We show that P (τ0 ≤ T ) > 0 for all T , give the probability of ultimate ruin, and establish asymptotics i...

In this paper we study the joint ruin problem for two insurance companies that divide between them both claims and premia in some specified proportions (modeling two branches of the same insurance company or an insurance and re-insurance company). Modeling the risk processes of the insurance companies by Cramér-Lundberg processes we obtain the Laplace transform in space of the probability that ...

Consider a discrete-time risk model in which the insurer is allowed to invest a proportion of its wealth in a risky stock and keep the rest in a risk-free bond. Assume that the claim amounts within individual periods follow an autoregressive process with heavy-tailed innovations and that the log-returns of the stock follow another autoregressive process, independent of the former one. We derive...

We study an elementary two-player card game where in each round players compare cards and the holder of the card with the smaller value wins. Using the rate equations approach, we treat the stochastic version of the game in which cards are drawn randomly. We obtain an exact solution for arbitrary initial conditions. In general, the game approaches a steady state where the card value densities o...

In this paper we consider an insurance company selling life insurance policies. New policies are sold at random points in time, and each policy stays active for a random amount of time, during which the policyholder pays premiums continuously at rate r. When the policy expires, the insurance company pays a claim of random size. The aim is to compute the probability of eventual ruin starting wit...