In any classical risk model one of the important random variable is time to ruin. As time to ruin warns the management for possible adverse situations that may arise, the distribution of time to ruin place a vital role in the day to day transactions of the any insurance company. Moments of the distribution are also important as coefficient of skewness of the distribution is very important in ac...

In this paper we consider a compound Poisson risk model where the insurer earns credit interest at a constant rate if the surplus is positive and pays out debit interest at another constant rate if the surplus is negative. Absolute ruin occurs at the moment when the surplus first drops below a critical value (a negative constant). We study the asymptotic properties of the absolute ruin probabil...

We present a simple discrete–time model of a risk process in which primary claims are followed by secondary claims representing after-effects. It is shown that the resulting discrete–time process is associated. Estimates for finite and infinite horizon ruin probabilities are then obtained via a diffusion approximation that is based on the classic Functional Central Limit Theorem of Newman and W...

The contribution of this paper is two-fold. First, we show that mutual fund theorems hold when minimizing the probability of lifetime ruin (that is, wealth reaching zero before death), as they do when maximizing the utility of consumption (Merton, 1971). Bayraktar and Young (2007a) determine when the investment strategies are identical under the two problems of maximizing utility of consumption...

Abstract. In this work, we investigate a multi-risk model describing insurance business with two or more independent series of claim amounts. Each series of claim amounts consists of independent nonnegative random variables. Claims of each series occur periodically with some fixed inter-arrival time. Claim amounts occur until they can be compensated by a common premium rate and the initial insu...

Abstract: We consider three closely related problems in optimal control: (1) minimizing the probability of lifetime ruin when the rate of consumption is stochastic and when the individual can invest in a Black-Scholes financial market; (2) minimizing the probability of lifetime ruin when the rate of consumption is constant but the individual can invest in two risky correlated assets; and (3) a ...

In this paper we compute the conditional and unconditional probability of ruin for an individual who wishes to consume a fixed periodic amount from an initial endowment invested in a portfolio earning a stochastic rate of return. The conditional probability of ruin is the probability that the net wealth becomes zero prior to the individual 's stochastic date of death. Unconditional is the proba...