Ruin Probability Of Risk Model Research Articles

Uniform Asymptotics for Finite-Time Ruin Probabilities of Risk Models with Non-Stationary Arrivals and Strongly Subexponential Claim Sizes

This paper considers the one- and two-dimensional risk models with a non-stationary claim-number process. Under the assumption that the claim-number process satisfies the large deviations principle, the uniform asymptotics for the finite-time ruin probability of a one-dimensional risk model are obtained for the strongly subexponential claim sizes. Further, as an application of the result of one-dimensional risk model, we derive the uniform asymptotics for a kind of finite-time ruin probability in a two dimensional risk model sharing a common claim-number process which satisfies the large deviations principle.

Asymptotics of the finite-time ruin probability of dependent risk model perturbed by diffusion with a constant interest rate

This paper considers a dependent risk model perturbed by diffusion with a constant interest rate, in which the claim sizes and the inter-arrival times have some dependence structures. When the claim sizes have a dominated varying-tailed distribution, the asymptotics of the finite-time ruin probability of the risk model have been obtained, which shows that the asymptotics of the finite-time ruin probability is insensitive to the perturbed term.

The finite-time ruin probability of a risk model with stochastic return and Brownian perturbation

This paper investigates a renewal risk model with stochastic return and Brownian perturbation, where the price process of the investment portfolio is described as a geometric Levy process. When the claim sizes have a subexponential distribution, we derive the asymptotics for the finite-time ruin probability of the above risk model. The obtained result confirms that the asymptotics for the finite-time ruin probability of the risk model with heavy-tailed claim sizes are insensitive to the Brownian perturbation.

A note on the finite-time ruin probability of a renewal risk model with Brownian perturbation

In this note, we consider a renewal risk model with constant force of interest and Brownian perturbation. Assuming that the claim-size distribution function is from the subexponential class, we derive for the finite-time ruin probability a precise asymptotic expansion, which holds uniformly for any finite time horizon. Our result confirms the intuition that the asymptotic ruin probabilities of risk models with heavy-tailed claims are insensitive to the Brownian perturbation.

Strong stability in a two-dimensional classical risk model with independent claims

In this paper, we study the strong stability of ruin probabilities in risk models. The question of stability naturally arises in risk theory since the governing parameters in these models can only be estimated with uncertainty. Moreover, in most cases there are not explicit expressions known for the ruin probabilities. Our objective is to present the applicability of the strong stability method to the bivariate classical risk model with independent claims. After clarifying the conditions to approximate the two-dimensional risk model with disturbance parameters by the two-dimensional classical risk model, we obtain the stability inequalities with an exact computation of the constants.