# Colloquium

## Subexponential Tails of Stochastically Discounted Aggregate Claims

### Qihe Tang

Department of Statistics and Actuarial Science, University of Iowa

*Thursday* March 18 at *12:30pm*, EMS E495A

We consider the classical risk model in which claims, arriving according to a homogenous Poisson process, form a sequence of independent random variables with common subexponential distribution. The insurer is allowed to make risk-free and risky investments and the price process of the investment portfolio is modeled as a general positive stochastic process independent of the insurance process. We derive an exact asymptotic formula for the tail probability of stochastically discounted aggregate claims by a fixed time. In doing so, we discover some properties of subexponential distributions, which are of independent interest

**Refeshments will be served after the talk at 1:30 in EMS E495B**