Abstract: In this work, we introduce the qualitative and
quantitative concept of the strong stability method in the risk process
modeling two lines of business of the same insurance company or
an insurance and re-insurance companies that divide between them
both claims and premiums with a certain proportion. The approach
proposed is based on the identification of the ruin probability
associate to the model considered, with a stationary distribution of a
Markov random process called a reversed process. Our objective, after clarifying the condition and the perturbation
domain of parameters, is to obtain the stability inequality of the ruin
probability which is applied to estimate the approximation error of a
model with disturbance parameters by the considered model. In the
stability bound obtained, all constants are explicitly written.
Abstract: In this paper, we study the performance of the strong
stability method of the univariate classical risk model. We interest to
the stability bounds established using two approaches. The first based
on the strong stability method developed for a general Markov chains.
The second approach based on the regenerative processes theory . By
adopting an algorithmic procedure, we study the performance of the
stability method in the case of exponential distribution claim amounts.
After presenting numerically and graphically the stability bounds, an
interpretation and comparison of the results have been done.
Abstract: 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 equation).
Application of our findings has been given through a simulation study.
Abstract: In this paper, we extend the compound binomial model to the case where the premium income process, based on a binomial process, is no longer a linear function. First, a mathematically recursive formula is derived for non ruin probability, and then, we examine the expected discounted penalty function, satisfy a defect renewal equation. Third, the asymptotic estimate for the expected discounted penalty function is then given. Finally, we give two examples of ruin quantities to illustrate applications of the recursive formula and the asymptotic estimate for penalty function.
Abstract: In this paper, a Markovian risk model with two-type claims is considered. In such a risk model, the occurrences of the two type claims are described by two point processes {Ni(t), t ¸ 0}, i = 1, 2, where {Ni(t), t ¸ 0} is the number of jumps during the interval (0, t] for the Markov jump process {Xi(t), t ¸ 0} . The ruin probability ª(u) of a company facing such a risk model is mainly discussed. An integral equation satisfied by the ruin probability ª(u) is obtained and the bounds for the convergence rate of the ruin probability ª(u) are given by using key-renewal theorem.
Abstract: This paper studies ruin probabilities in two discrete-time
risk models with premiums, claims and rates of interest modelled by
three autoregressive moving average processes. Generalized Lundberg
inequalities for ruin probabilities are derived by using recursive
technique. A numerical example is given to illustrate the applications
of these probability inequalities.