The purpose of this paper is to explore a discrete-time cash flow optimization problem the insurance company with time value ruin under different interest rates. For sake considering ruin, we assume that shareholders can get subsidies per unit time, as long not bankrupt. switching rates on market controlled by stationary Markov chain. dynamic programming principle used solve problem. By using m...

We study the expected time to ruin in a risk process in which dividends are paid when the surplus is above the barrier. We consider the case in which the dividend rate is smaller than the premium rate. We obtain results for the classical compound Poisson risk process with phase-type claim size. When the ruin probability is 1, we derive the expected time to ruin and the expected dividends paid. ...

We consider a compound Poisson risk model where part of the premium is paid to the shareholders as dividends when the surplus exceeds a specified threshold level. In this model, we are interested in computing the moments of the total discounted dividends paid until ruin occurs. However, instead of employing the traditional argument which involves conditioning on the time and amount of the first...

Risk processes are considered, which locally behave as a Brownian motion with some drift and variance, both depending on an underlying Markov chain that is used also to generate the claims arrival process. Thus claims arrive according to a renewal process with waiting times of phase-type. The claims are assumed to form an iid sequence, independent of everything else, and with a distribution wit...

This paper investigates the finiteand infinite-time ruin probabilities in a discrete-time stochastic economic environment. Under the assumption that the insurance risk – the total net loss within one time period – is extended-regularly-varying tailed or rapidly-varying tailed, various precise estimates for the ruin probabilities are derived. In particular, some estimates obtained are uniform wi...

This article considers the problem of evaluating infinite-time (or finite-time) ruin probability under a given compound Poisson surplus process by approximating the claim size distribution by a finite mixture exponential, say Hyperexponential, distribution. It restates the infinite-time (or finite-time) ruin probability as a solvable ordinary differential equation (or a partial differential equ...