Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model
نویسندگان
چکیده
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 asymptotic formula holds for the nite-time and in nite-time ruin probabilities. Restricting our attention to the so-called constant investment strategy, we show how the insurer adjusts his investment portfolio to maximize the expected terminal wealth subject to a constraint on the ruin probability. Keywords: Asymptotics; Constant investment strategy; Lévy process; Portfolio optimization; Regular variation; Ruin probability; Uniformity. Mathematics Subject Classi cation: Primary 91B30; Secondary 60G51, 60K05, 91B28
منابع مشابه
Uniform 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 کاملNumerical Algorithm for the Stochastic Present Value of Aggregate Claims in the Renewal Risk Model
For the stochastic present value of aggregate claims in the renewal risk model, a numerical algorithm is constructed based on the Monte Carlo and random process principle. The basic idea and design process of this algorithm is detailed. The numerical simulation results show that it is consistence with the theory analysis result under different parameter different distribution. The numerical alg...
متن کاملRuin Probabilities for Risk Processes with Non-stationary Arrivals and Subexponential Claims
In this paper, we obtain the finite-horizon and infinite-horizon ruin probability asymptotics for risk processes with claims of subexponential tails for non-stationary arrival processes that satisfy a large deviation principle. As a result, the arrival process can be dependent, non-stationary and nonrenewal. We give three examples of non-stationary and non-renewal point processes: Hawkes proces...
متن کاملA uniform asymptotic estimate for discounted aggregate claims with subexponential tails
In this paper we study the tail probability of discounted aggregate claims in a continuous-time renewal model. For the case that the common claim-size distribution is subexponential, we obtain an asymptotic formula, which holds uniformly for all time horizons within a finite interval. Then, with some additional mild assumptions on the distributions of the claim sizes and inter-arrival times, we...
متن کاملHeavy Tails of Discounted Aggregate Claims in the Continuous-time Renewal Model
We study the tail behavior of discounted aggregate claims in a continuous-time renewal model. For the case of Pareto-type claims, we establish a tail asymptotic formula, which holds uniformly in time.
متن کامل