Assume that the surplus of an insurer follows a jump­diffusion process and the insurer would invest its surplus in a risky asset, whose prices are modelled by a geometric Brow­ nian motion. The resulting surplus for the insurer is called as a jump­diffusion surplus process compounded by the geometric Brownian motion. In this resulting surplus process, ruin may be caused by a claim or by oscilla...

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...

 This paper mainly considers a nonstandard risk model with a constant interest rate‎, ‎where both the claim sizes and the inter-arrival times follow some certain dependence structures‎. ‎When the claim sizes are dominatedly varying-tailed‎, ‎asymptotics for the infinite time ruin probability of the above dependent risk model have been given‎.

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 consider a risk model with threshold strategy, where the insurance company pays off a certain percentage of the income as dividend whenever the current surplus is larger than a given threshold. We investigate the ruin time, ruin probability and the total dividend, using methods and results from queueing theory.