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.

This article considers the problem of evaluating infinite-time (or finite-time) ruin probability under a given compound Poisson surplus process by approximating the claim size distribution by a finite mixture exponential, say Hyperexponential, distribution. It restates the infinite-time (or finite-time) ruin probability as a solvable ordinary differential equation (or a partial differential equ...

 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 compute ruin probabilities, in both infinite-time and finite-time, for a Gambler’s Ruin problem with both catastrophes and windfalls in addition to the customary win/loss probabilities. For constant transition probabilities, the infinite-time ruin probabilities are derived using difference equations. Finite-time ruin probabilities of a system having constant win/loss probabilities and variab...

This article considers the problem of evaluating infinite-time (or finite-time) ruin probability under a given compound Poisson surplus process. By approximating the claim size distribution by a finite mixture exponential, say Hyperexponential, distribution. It restates the infinite-time (or finitetime) ruin probability as a solvable ordinary differential equation (or a partial differential equ...

In this paper we consider the probabilities of finiteand infinite-time absolute ruin in the renewal risk model with constant premium rate and constant force of interest. In the particular case of compound Poisson model, explicit asymptotic expressions for the finiteand infinite-time absolute ruin probabilities are given. For the general renewal risk model, we present an asymptotic expression fo...

Infinite Time Ruin Probability in the Individual Risk Model with Dependent Structure for Light and Heavy Tailed Distributions