Perturbed Compound Poisson Risk Model Research Articles

The Perturbed Compound Poisson Risk Model with Proportional Investment

The Perturbed Compound Poisson Risk Model with Proportional Investment

On a perturbed compound Poisson risk model under a periodic threshold-type dividend strategy

In this paper, we model the insurance company's surplus flow by a perturbed compound Poisson model. Suppose that at a sequence of random time points, the insurance company observes the surplus to decide dividend payments. If the observed surplus level is larger than the maximum of a threshold $ b>0 $ and the last observed level (after dividends payment if possible), then a fraction $ 0<\theta<1 $ of the excess amount is paid out as a lump sum dividend. We assume that the solvency is also discretely monitored at these observation times, so that the surplus process stops when the observed value becomes negative. Integro-differential equations for the expected discounted dividend payments before ruin and the Gerber-Shiu expected discounted penalty function are derived, and solutions are also analyzed by Laplace transform method. Numerical examples are given to illustrate the applicability of our results.

Moments of discounted dividend payments in a risk model with randomized dividend-decision times

We consider a perturbed compound Poisson risk model with randomized dividend-decision times. Different from the classical barrier dividend strategy, the insurance company makes decision on whether or not paying off dividends at some discrete time points (called dividend-decision times). Assume that at each dividend-decision time, if the surplus is larger than a barrier b > 0; the excess value will be paid off as dividends. Under such a dividend strategy, we study how to compute the moments of the total discounted dividend payments paid off before ruin.

Ruin probabilities for a perturbed risk model with stochastic premiums and constant interest force

In this paper, we consider a perturbed compound Poisson risk model with stochastic premiums and constant interest force. We obtain the upper bound and Lundberg-Cramér approximation for the infinite-time ruin probability, and consider the asymptotic formula for the finite-time ruin probability when the claim size is heavy-tailed. We show that the model in our paper has similar results to the classical risk process and some existing generalized models.

The optimal dividend barrier in the perturbed compound Poisson risk model with randomized observation time

This paper considers the dividend problems in the perturbed compound Poisson risk model. Assume that dividends can only be paid at the observation time when the surplus exceeds the barrier level and the excess is paid as dividend. In this paper, integro-differential equations for the expected discounted dividends until ruin and the Laplace transform of ruin time are firstly derived. When the claim is exponentially distributed, explicit expressions for the expected discounted dividends until ruin and the Laplace transform of ruin time are also obtained. Finally, the optimal dividend barrier which maximizes the expected discounted dividends until ruin is given.

Some results on absolute ruin in the perturbed insurance risk model with investment and debit interests

In this paper, we consider a perturbed compound Poisson risk model with investment and debit interests. Dividends are paid to the shareholders according to a threshold dividend strategy. An alternative assumption is that when the surplus is negative, a debit interest is applied and when the surplus is above a certain positive level, the insurer could earn investment interest. Integro-differential equations with boundary conditions satisfied by the moment-generating function, the nth moment of the present value of all dividends until absolute ruin and the Gerber–Shiu expected discounted penalty function are obtained. Then, we present the explicit expressions for the zero discounted nth moment of the present value of all dividends until absolute ruin in the case of exponential claims. Finally, numerical example is also given to illustrate the effect of the related parameters on the first moment of the present value of all dividends until absolute ruin.

The perturbed compound Poisson risk model with linear dividend barrier

In this paper, we consider a diffusion perturbed classical compound Poisson risk model in the presence of a linear dividend barrier. Partial integro-differential equations for the moment generating function and the nth moment of the present value of all dividends until ruin are derived. Moreover, explicit solutions for the nth moment of the present value of dividend payments are obtained when the individual claim size distribution is exponential. We also provided some numerical examples to illustrate the applications of the explicit solutions. Finally we derive partial integro-differential equations with boundary conditions for the Gerber–Shiu function.

The perturbed compound Poisson risk model with constant interest and a threshold dividend strategy

In this paper, we consider the compound Poisson risk model perturbed by diffusion with constant interest and a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generation function and the n th moment of the present value of all dividends until ruin are derived. We also derive integro-differential equations with boundary conditions for the Gerber–Shiu functions. The special case that the claim size distribution is exponential is considered in some detail.

The perturbed compound Poisson risk model with two-sided jumps

In this paper, we consider a perturbed compound Poisson risk model with two-sided jumps. The downward jumps represent the claims following an arbitrary distribution, while the upward jumps are also allowed to represent the random gains. Assuming that the density function of the upward jumps has a rational Laplace transform, the Laplace transforms and defective renewal equations for the discounted penalty functions are derived, and the asymptotic estimate for the probability of ruin is also studied for heavy-tailed downward jumps. Finally, some explicit expressions for the discounted penalty functions, as well as numerical examples, are given.

A note on the perturbed compound poisson risk model with a threshold dividend strategy

In this paper, we consider the Perturbed Compound Poisson Risk Model with a threshold dividend strategy (PCT). Integro-differential equations (IDE) for its Gerber-Shiu functions and dividend payments function are stated. We maily focus on deriving the boundary conditions to solve these equations.

The dividend function in the jump-diffusion dual model with barrier dividend strategy

A dual model of the perturbed classical compound Poisson risk model is considered under a constant dividend barrier. A new method is used in deriving the boundary condition of the equation for the expectation function by studying the local time of a related process. We obtain the expression for the expected discount dividend function in terms of those in the corresponding perturbed compound Poisson risk model without barriers. A special case in which the gain size is phase-type distributed is illustrated. We also consider the existence of the optimal dividend level.

The perturbed compound Poisson risk model with multi-layer dividend strategy

In this paper, we consider a perturbed compound Poisson risk model with multi-layer dividend strategy. Integro-differential and integral equations for the expected discounted penalty function are derived and solved. When the claims are subexponentially distributed, the asymptotic formula for ruin probability is obtained.