CLASSICAL RISK MODEL WITH THRESHOLD DIVIDEND STRATEGY

In this article, a threshold dividend strategy is used for classical risk model. Under this dividend strategy, certain probability of ruin, which occurs in case of constant barrier strategy, is avoided. Using the strong Markov property of the surplus process and the distribution of the deficit in classical risk model, the survival probability for this model is derived, which is more direct than that in Asmussen（2000, P195, Proposition 1.10）. The occupation time of non-dividend of this model is also discussed by means of Martingale method.

The compound Poisson risk model with dependence under a multi-layer dividend strategy

In this paper, a compound Poisson risk model with time-dependent claims is studiedunder a multi-layer dividend strategy. A piecewise integro-differential equation for the Gerber- Shiu function is derived and solved. Asymptotic formulas of the ruin probability are obtained when the claim size distributions are heavy-tailed.

Optimal Dividend Strategy in Compound Binomial Model with Bounded Dividend Rates

We consider the compound binomial model, and assume that dividends are paid to the shareholders according to an admissible strategy with dividend rates bounded by a constant.The company controls the amount of dividends in order to maximize the cumulative expected discounted dividends prior to ruin. We show that the optimal value function is the unique solution of a discrete HJB equation. Moreover, we obtain some properties of the optimal payment strategy, and offer a simple algorithm for obtaining the optimal strategy. The key of our method is to transform the value function. Numerical examples are presented to illustrate the transformation method.

A Class of Delayed Renewal Risk Processes with a Threshold Dividend Strategy

This paper considers a class of delayed renewal risk processes with a threshold dividend strategy. The main result is an expression of the Gerber-Shiu expected discounted penalty function in the delayed renewal risk model in terms of the corresponding Cerber-Shiu function in the ordinary renewal model. Subsequently, this relationship is considered in more detail in both the stationary renewal risk model and the ruin probability.

The Phase-type Risk Model Perturbed by Diffusion under a Threshold Dividend Strategy

This paper considers a perturbed renewal risk process in which the inter-claim times have a phasetype distribution under a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generating function and the ruth moment of the present value of all dividends until ruin are derived. Explicit expressions for the expectation of the present value of all dividends until ruin are obtained when the claim amount distribution is from the rational family. Finally, we present an example.

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 Cerber-Shiu functions and dividend payments function are stated. We maily focus on deriving the boundary conditions to solve these equations.

The Markov-Dependent Risk Model with a Threshold Dividend Strategy

This paper studies a Markov-dependent risk model in which the claim occurrence and the claim amount are regulated by an external discrete time Markov process. Integro-differential equations in matrix form for the Gerber-Shiu discounted penalty function are presented. Then the analytical solutions to the equations are derived. Finally, in the two-state model, some numerical results are obtained when claim amount is exponentially distributed.

Equilibrium dividend strategies in the dual model with a random time horizon

This paper investigates the dividend problem with non-exponential discounting in a dual model.We assume that the dividends can only be paid at a bounded rate and that the surplus process is killed by an exponential random variable.Since the non-exponential discount function leads to a time inconsistent control problem,we study the equilibrium HJB-equation and give the associated verification theorem.For the case of a mixture of exponential discount functions and exponential gains,we obtain the explicit equilibrium dividend strategy and the corresponding equilibrium value function.Besides,numerical examples are shown to illustrate our results.

Optimal Dividend-Equity Issuance Strategy in a Dual Model with Fixed and Proportional Transaction Costs

In this paper, we consider the problem of optimal dividend payout and equity issuance for a company whose liquid asset is modeled by the dual of classical risk model with diffusion. We assume that there exist both proportional and fixed transaction costs when issuing new equity. Our objective is to maximize the expected cumulative present value of the dividend payout minus the equity issuance until the time of bankruptcy,which is defined as the first time when the company＇s capital reserve falls below zero. The solution to the mixed impulse-singular control problem relies on two auxiliary subproblems： one is the classical dividend problem without equity issuance, and the other one assumes that the company never goes bankrupt by equity issuance.We first provide closed-form expressions of the value functions and the optimal strategies for both auxiliary subproblems. We then identify the solution to the original problem with either of the auxiliary problems. Our results show that the optimal strategy should either allow for bankruptcy or keep the company＇s reserve above zero by issuing new equity, depending on the model＇s parameters. We also present some economic interpretations and sensitivity analysis for our results by theoretical analysis and numerical examples.

Dividend Payments with a Threshold Strategy in a Markov-Dependent Risk Model

In this paper,a Markov-dependent risk model with a threshold strategy is considered. The expected discounted dividend payments satisfy some integro-differential equations. The analytical solutions to these systems are given. Finally,some numerical exam-ples in some special cases are provided.

On Optimality of the Barrier Strategy for the Classical Risk Model with Interest

In this paper, we consider the optimal dividend problem for a classical risk model with a constant force of interest. For such a risk model, a sufficient condition under which a barrier strategy is the optimal strategy is presented for general claim distributions. When claim sizes are exponentially distributed, it is shown that the optimal dividend policy is a barrier strategy and the maximal dividend-value function is a concave function. Finally, some known results relating to the distribution of aggregate dividends before ruin are extended.

Optimal Dividend Strategies in a Double Compound Poisson Risk Process

In this paper, we consider a double compound Poisson risk model involving two independent classes ofinsurance risks with a threshold dividend strategy. We derived the integro-differential equations （IDE） with certain boundary conditions for the present value of dividends until ruin. When the claims from both classes are exponentially distributed, we show that the threshold dividend strategy is an optimal dividend strategy.

The Maximum Surplus before Ruin and Related Problems in a Jump-Diffusion Renewal Risk Process

In this paper, we investigate a Sparre Andersen risk model perturbed by diffusion with phase-type inter-claim times. We mainly study the distribution of maximum surplus prior to ruin. A matrix form of integro-differential equation for this quantity is derived, and its solution can be expressed as a linear combination of particular solutions of the corresponding homogeneous integro-differential equations. By using the divided differences technique and nonnegative real part roots of Lundberg＇s equation, the explicit Laplace transforms of particular solutions are obtained. Specially, we can deduce closed-form results as long as the individual claim size is rationally distributed. We also give a concise matrix expression for the expected discounted dividend payments under a barrier dividend strategy. Finally, we give some examples to present our main results.