Consider a two-dimensional delayed renewal risk model with a constant interest rate, where the claim sizes of the two classes form a sequence of independent and identically distributed random vectors following a common bivariate Sarmanov distribution. In the presence of heavytailed claim sizes, some asymptotic formulas are derived for the finite-time and infinite-time ruin probabilities.

The increasing risk of poverty in retirement has been well-documented; it is projected that current and future retirees’ living expenses will significantly exceed their savings and income. In this paper, we consider a retiree who does not have sufficient wealth and income to fund her future expenses and we seek the asset allocation that minimizes the probability of financial ruin during her lif...

We consider a rm that is faced with an uncontrollable stochastic cash ow, or random risk process. There is one investment opportunity, a risky stock, and we study the optimal investment decision for such rms. There is a fundamental incompleteness in the market, in that the risk to the investor of going bankrupt can not be eliminated under any investment strategy, since the random risk process e...

We focus on numerical evaluation of some quantities of interest in ruin theory, and on the practical use of the fast Fourier transform algorithm (FFT) in this context. We discuss the general application of the FFT for stochastic models, and we illustrate this by looking again at the probability of ruin in the classical risk model and by extending this approach to evaluation of the first moment ...

A risk process with constant premium rate c and Poisson arrivals of claims is considered. A threshold r is defined for claim interarrival times, such that if k consecutive interarrival times are larger than r, then the next claim has distribution G. Otherwise, the claim size distribution is F . Asymptotic expressions for the infinite horizon ruin probabilities are given for both lightand the he...

In this paper, we consider a two-dimensional risk process in which the companies split each claim and premium fixed proportion. It serves as classical framework of quota-share reinsurance contract for given business line. Such reduces insurer’s exposure to liabilities created through its underwriting activities. For analyzed model, derive joint infinite-time ruin probability formula exponential...

In ruin theory, the univariate model may be found too restrictive to describe accurately the complex evolution of the reserves of an insurance company. In the case where the company is composed of multiple lines of business, we compute asymptotics of finite-time ruin probabilities. Capital transfers between lines are partially allowed. When claim amounts are regularly varying distributed, sever...