On Ruin Probability and Aggregate Claim Representations for Pareto Claim Size Distributions
نویسندگان
چکیده
We generalize an integral representation for the ruin probability in a Crámer-Lundberg risk model with shifted (or also called US-)Pareto claim sizes, obtained by Ramsay [14], to classical Pareto(a) claim size distributions with arbitrary real values a > 1 and derive its asymptotic expansion. Furthermore an integral representation for the tail of compound sums of Pareto-distributed claims is obtained and numerical illustrations of its performance in comparison to other aggregate claim approximations are provided.
منابع مشابه
Of Some Ruin Theory Results B ¥
The paper deals with the renewal equation governing the infinite-time ruin probability. It is emphasized as intended to be no more than a pleasant ramble through a few scattered results. An interesting connection between ruin probability and a recurslon formula for computation of the aggregate claims distribution is noted and discussed. The relation between danger of the claim size distribution...
متن کاملAsymptotics for the infinite time ruin probability of a dependent risk model with a constant interest rate and dominatedly varying-tailed claim sizes
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.
متن کاملUniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model
Consider an insurer who is allowed to make risk-free and risky investments. The price process of the investment portfolio is described as a geometric Lévy process. We study the tail probability of the stochastic present value of future aggregate claims. When the claim-size distribution is of Pareto type, we obtain a simple asymptotic formula which holds uniformly for all time horizons. The same...
متن کاملRuin Probabilities and Aggregrate Claims Distributions for Shot Noise Cox Processes
We consider a risk process Rt where the claim arrival process is a superposition of a homogeneous Poisson process and a Cox process with a Poisson shot noise intensity process, capturing the effect of sudden increases of the claim intensity due to external events. The distribution of the aggregate claim size is investigated under these assumptions. For both light-tailed and heavy-tailed claim s...
متن کاملUniform Asymptotics for Discounted Aggregate Claims in Dependent Risk Models
In this paper, we consider some non-standard renewal risk models with some dependent claim sizes and stochastic return, where an insurance company is allowed to invest her/his wealth in financial assets, and the price process of the investment portfolio is described as a geometric Lévy process. When the claim-size distribution belongs to some classes of heavy-tailed distributions and a constrai...
متن کامل