The Expected Discounted Penalty Function (EDPF) was introduced in a series of now classical papers [Gerber, H.U., Shiu, E.S.W., 1997. The joint distribution of the time of ruin, the surplus immediately before ruin, and the deficit at ruin. Insurance: Math. Econ. 21, 129–137; Gerber, H.U., Shiu, E.S.W., 1998a. On the time value of ruin. N. Am. Actuar. J. 2 (1), 48–78; Gerber, H.U., Shiu, E.S.W.,...

We study a family of diffusion models for compounded risk reserves, which account for the investment income earned and for the inflation experienced on claim amounts. We are interested in the models which the dividend payments are paid from the risk reserves. After defining the process of conditional probability over finite time, the classical diffusion processes results turn the nonlinear stoc...

Abstract: We consider three closely related problems in optimal control: (1) minimizing the probability of lifetime ruin when the rate of consumption is stochastic and when the individual can invest in a Black-Scholes financial market; (2) minimizing the probability of lifetime ruin when the rate of consumption is constant but the individual can invest in two risky correlated assets; and (3) a ...

Optimal dividend payment under a ruin constraint is a two objective control problem 1 which – in simple models – can be solved numerically by three essentially different methods. One 2 is based on a modified Bellman equation and the policy improvement method (see (2003)). In this 3 paper we use explicit formulas for running allowed ruin probabilities which avoid a complete search 4 and speed up...

This paper is concerned with an insurance risk model whose claim process is described by a Lévy subordinator process. Lévy-type risk models have been the object of much research in recent years. Our purpose is to present, in the case of a subordinator, a simple and direct method for determining the finite time (and ultimate) ruin probabilities, the distribution of the ruin severity, the reserve...

 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.

We consider the dynamic proportional reinsurance in a two-dimensional compound Poisson risk model. The optimization in the sense of minimizing the ruin probability which is defined by the sum of subportfolio is being ruined. Via the Hamilton-Jacobi-Bellman approach we find a candidate for the optimal value function and prove the verification theorem. In addition, we obtain the Lundberg bounds a...

We study the probability of ruin before time t for the family of tempered stable Lévy insurance risk processes, which includes the spectrally positive inverse Gaussian processes. Numerical approximations of the ruin time distribution are derived via the Laplace transform of the asymptotic ruin time distribution, for which we have an explicit expression. These are benchmarked against simulations...

This article provides importance sampling algorithms for computing the probabilities of various types ruin of spectrally negative Lévy risk processes, which are ruin over the infinite time horizon, ruin within a finite time horizon and ruin past a finite time horizon. For the special case of the compound Poisson process perturbed by diffusion, algorithms for computing probabilities of ruins by ...