We consider the capital of an insurance company that employs reinsurance. The reinsurer is assumed to have infinite sources of capital. The reinsurer covers part of the claims, but in return it receives a certain part of the income from premiums of the insurance company. In addition, the reinsurer receives some of the dividends that are withdrawn when a certain surplus level b is reached. A spe...

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...

Numerical evaluation of ruin probabilities in the classical risk model is an important problem. If claim sizes are heavy-tailed, then such evaluations are challenging. To overcome this, an attractive way is to approximate the claim sizes with a phase-type distribution. What is not clear though is how many phases are enough in order to achieve a specific accuracy in the approximation of the ruin...

We consider that the surplus of an insurer follows compound Poisson process and the insurer would invest its surplus in risky assets, whose prices satisfy the Black-Scholes model. In the risk process, we decompose the ruin probability into the sum of two ruin probabilities which are caused by the claim and the oscillation, respectively. We derive the integro-differential equations for these rui...

Based on characteristics of the nonlife joint-stock insurance company, this paper presents a compound binomial risk model that randomizes the premium incomeonunit time and sets the thresholdx for paying dividends to shareholders. In thismodel, the insurance company obtains the insurance policy in unit time with probability p 0 and pays dividends to shareholders with probability p 1 when the sur...

Based on Invariance Principle for Brownian Motion, we obtained a closed-form expression of the ruin probability Discrete-Time Risk Model with Random Premiums that was recently introduced by Korzeniowski [1]. We show in this model, given two strategies have same ultimate ruin, strategy larger initial capital and smaller loading factor is less risky than it lowers finite time horizon.

Let C1, C2, . . . , Cm be independent subordinators with finite expectations and denote their sum by C. Consider the classical risk process X(t) = x+ct−C(t). The ruin probability is given by the well known Pollaczek-Hinchin formula. If ruin occurs, however, it will be caused by a jump of one of the subordinators whose sum constitutes C. Formulae for the probability that ruin is caused by Ci are...

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...

Consider two insurance companies (or two branches of the same company) that divide between them both claims and premia in some specified proportions. We model the occurrence of claims according to a renewal process. One ruin problem considered is that of the corresponding two-dimensional risk process first leaving the positive quadrant; another is that of entering the negative quadrant. When th...