Constant dividend barrier in a risk model with interclaim-dependent claim sizes

On a class of renewal risk models with a constant dividend barrier

This paper considers a new risk model with a constant dividend barrier, which the claim amount affected by a threshold value. The hypothesis of the model is presented and the integro-differential equation for the Gerber-Shiu penalty function is given. Then the linear solution of the Gerber-Shiu discounted penalty function is figured out. The paper also derives the integro-differential equation and the linear solution of the expected discounted dividend payments. An example is given too.

The Gerber-Shiu discounted penalty function is considered for a class of delayed renewal risk processes. In (Willmot 2004), special cases of the model include the stationary renewal risk model and the situation where the time until the first claim is exponentially distributed. In this paper, we consider a class of delayed and perturbed risk model with dependence between interclaim arrivals and claim sizes. The integro-differential equations for the Gerber-Shiu discounted penalty functions are derived.

On the probability of ruin in a Markov-modulated risk model

In this paper, the absolute ruin in the compound Poisson risk model with interest and a constant dividend barrier is investigated. First, integro-differential equations satisfied by the expected discounted dividend payments are derived. The explicit expressions are obtained when the individual claim size is exponential distributed. Second, the moment generating function of the discounted dividends is considered, and integro-differential equations satisfied by the moment generating function of the discounted dividends are derived. Third, by a “differential” argument, the time to recovery to zero from a given negative surplus is considered. Finally, how long it takes for the surplus process to reach the dividend barrier is discussed.

The Gerber–Shiu discounted penalty function in the delayed renewal risk process with random income

On the expected discounted penalty function in a Markov-dependent risk model with constant dividend barrier

On the classical risk model with credit and debit interests under absolute ruin

In this paper, some results on the dividend payments prior to ruin in the classical surplus process with stochastic interest are derived. An integro-differential equation with a boundary conditions satisfied by the expected present value of dividend payments is derived and solved. Furthermore, closed-form expressions for exponential claims are given.

In this short paper, we show how fluctuation identities for Lévy processes with no positive jumps yield the distribution of the present value of dividends paid until ruin in a Lévy insurance risk model with a dividend barrier.

In this paper, a discrete Markov-modulated risk model with delayed claims, random premium income, and a constant dividend barrier is proposed. It is assumed that the random premium income and individual claims are affected by a Markov chain with finite state space. The model proposed is an extension of the discrete semi-Markov risk model with random premium income and delayed claims. Explicit expressions for the total expected discounted dividends until ruin are obtained by the method of generating function and the theory of difference equations. Finally, the effect of related parameters on the total expected discounted dividends are shown in several numerical examples.

Insurance policies usually involve factors with greater risk of claims are charged at a higher rate. Therefore having efficient risk models is very important for insurers in estimating risk of insurance policies. Statistical methods and models for count data can be used to analyse or determine such insurance policy’s levels. In classical risk model, the claim numbers are usually determined by the underling risk of only one class. However, insurance businesses generally have more than one class of businesses. In recent year, many researchers are interested in studying risk models that the claim number is determined by exterior risk which affects more than one class. Therefore, the concept of common shock risk model is introduced. The common shock risk models originally assume the Poisson distribution. However, the property of having equal mean and variance of the Poisson distributions may not hold in some applications in particular when the data is over dispersed. Therefore, in this project, we construct common shock risk models based on negative binomial time series to study risk of any business where the claim numbers in the two classes of business may not be independent. In this study, we derive some probabilistic properties and the upper bound of the ruin probability. Moreover, numerical calculations of ruin probability in different cases are provided.

This paper presents the Laplace transform of the time until ruin for a fairly general risk model. The model includes both the classical and most Sparre-Andersen risk models with phase-distributed claim amounts as special cases. It also allows for correlated arrival processes, and claim sizes that depend upon environmental factors such as periods of contagion. The paper exploits the relationship between the surplus process and fluid queues, where a number of recent developments have provided the basis for our analysis.

We find the optimal dividend strategy in two related risk models under an affine penalty for ruin. The first risk model is the classical Cramer–Lundberg risk model, and the second is the so-called dual risk model. Under both models, for exponentially distributed jumps, we show that the optimal dividend strategy is a barrier strategy and obtain the barrier explicitly. Moreover, we prove that the optimal barrier increases with respect to the parameters of the affine penalty, while the penalized value function decreases with respect to the penalty. We also compute the expected time until ruin and show that the expected time of ruin increases with respect to the parameters of the affine penalty. Finally, we present some numerical examples to demonstrate the relationship between the results for the classical and dual risk models. Our main contributions are in comparing the classical and dual risk models side-by-side and in obtaining explicit expressions for the penalized value functions, the optimal barriers, and the expected times of ruin. Also, we contrast the free-boundary condition associated with the barrier strategies in the two models.

Upper bounds for ultimate ruin probabilities in the Sparre Andersen risk model with interest and a nonlinear dividend barrier