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 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...

We compute ruin probabilities, in both infinite-time and finite-time, for a Gambler’s Ruin problem with both catastrophes and windfalls in addition to the customary win/loss probabilities. For constant transition probabilities, the infinite-time ruin probabilities are derived using difference equations. Finite-time ruin probabilities of a system having constant win/loss probabilities and variab...

Using an approach similar to that of Gerber and Shiu (1998), a recursive formula is given for the expected discounted penalty due at ruin, in the discrete time risk model. With it the joint distribution of three random variables is obtained; time to ruin, the surplus just before ruin and the deficit at ruin. The time to ruin is analyzed through its probability generating function (p.g.f.). The ...

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. ...

‎in this paper‎, ‎we consider the optimal asset control of a financial company which can control its liquid reserves by paying dividends and by issuing new equity‎. ‎we assume that the liquid surplus of the company in the absence of control is modeled by the diffusion model‎. ‎it is a hot topic to maximize the expected present value of dividends payout minus equity issuance until the time of ba...

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...

We consider a discrete-time dependent Sparre Andersen risk model which incorporates multiple threshold levels characterizing an insurer’s minimal capital requirement, dividend paying situations, and external financial activities. We focus on the development of a recursive computational procedure to calculate the finite-time ruin probabilities and expected total discounted dividends paid prior t...