EXPECTED PRESENT VALUE OF TOTAL DIVIDENDS IN THE COMPOUND BINOMIAL MODEL WITH DELAYED CLAIMS AND RANDOM INCOME

In this paper, a compound binomial model with a constant dividend barrier and random income is considered. Two types of individual claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim and may be delayed for one time period with a certain probability. The premium income is assumed to another binomial process to capture the uncertainty of the customer＇s arrivals and payments. A system of difference equations with certain boundary conditions for the expected present value of total dividend payments prior to ruin is derived and solved. Explicit results are obtained when the claim sizes are Kn distributed or the claim size distributions have finite support. Numerical results are also provided to illustrate the impact of the delay of by-claims on the expected present value of dividends.

RUIN PROBABILITY IN THE CONTINUOUS-TIME COMPOUND BINOMIAL MODEL WITH INVESTMENT

This article deals with the problem of minimizing ruin probability under optimal control for the continuous-time compound binomial model with investment. The jump mechanism in our article is different from that of Liu et al [4]. Comparing with [4], the introduction of the investment, and hence, the additional Brownian motion term, makes the problem technically challenging. To overcome this technical difficulty, the theory of change of measure is used and an exponential martingale is obtained by virtue of the extended generator. The ruin probability is minimized through maximizing adjustment coefficient in the sense of Lundberg bounds. At the same time, the optimal investment strategy is obtained.

Joint and supremum distributions in the compound binomial model with Markovian environment

In this paper, we study the compound binomial model in Markovian environment, which is proposed by Cossette, et al. （2003）. We obtain the recursive formula of the joint distributions of T, X（T - 1） and ｜X（T）｜（i.e., the time of ruin, the surplus before ruin and the deficit at ruin） by the method of mass function of up-crossing zero points, as given by Liu and Zhao （2007）. By using the same method, the recursive formula of supremum distribution is obtained. An example is included to illustrate the results of the model.

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.

THE COMPOUND BINOMIAL MODEL WITH A CONSTANT DIVIDEND BARRIER AND PERIODICALLY PAID DIVIDENDS

Consider the compound binomial risk model with interest on the surplus under a constant dividend barrier and periodically paying dividends. A system of integral equations for the arbitrary moments of the sum of the discounted dividend payments until ruin is derived. Moreover, under a very relaxed condition, the solutions for arbitrary moments are obtained by setting up iteration processes because of a special property of the system of integral equations.

On the Expected Present Value of Total Dividends in a Risk Model with Potentially Delayed Claims

In this paper, we consider a risk model in which two types of individual claims, main claims and by-claims, are defined. Every by-claim is induced by the main claim randomly and may be delayed for one time period with a certain probability. The dividend policy that certain amount of dividends will be paid as long as the surplus is greater than a constant dividend barrier is also introduced into this delayed claims risk model. By means of the probability generating functions, formulae for the expected present value of total dividend payments prior to ruin are obtained for discrete-type individual claims. Explicit expressions for the corresponding results are derived for K n claim amount distributions. Numerical illustrations are also given.

Finite Time Ruin Probabilities and Large Deviations for Generalized Compound Binomial Risk Models

In this paper, we extend the classical compound binomial risk model to the case where the premium income process is based on a Poisson process, and is no longer a linear function. For this more realistic risk model, Lundberg type limiting results for the finite time ruin probabilities are derived. Asymptotic behavior of the tail probabilities of the claim surplus process is also investigated.

The Gerber-Shiu Discounted Penalty Function for a Compound Binomial Risk Model with By-claims

A recursive formula of the Gerber-Shiu discounted penalty function for a compound binomial risk model with by-claims is obtained. In the discount-free case, an explicit formula is given. Utilizing such an explicit expression, we derive some useful insurance quantities, including the ruin probability, the density of the deficit at ruin, the joint density of the surplus immediately before ruin and the deficit at ruin, and the density of the claim causing ruin.

Some Large Deviation Results for Generalized Compound Binomial Risk Models

This paper is a further investigation of large deviation for partial and random sums of random variables, where {Xn,n ≥ 1} is non-negative independent identically distributed random variables with a common heavy-tailed distribution function F on the real line R and finite mean μ∈ R. {N(n),n ≥ 0} is a binomial process with a parameter p ∈ (0,1) and independent of {Xn,n ≥ 1}; {M(n),n ≥ 0} is a Poisson process with intensity λ > 0, Sn = ΣNn i=1 Xi-cM(n). Suppose F ∈ C, we futher extend and improve some large deviation results. These results can apply to certain problems in insurance and finance.

Ruin Probability and Joint Distributions of Some Actuarial Random Vectors in the Compound Pascal Model

The compound negative binomial model, introduced in this paper, is a discrete time version. We discuss the Markov properties of the surplus process, and study the ruin probability and the joint distributions of actuarial random vectors in this model. By the strong Markov property and the mass function of a defective renewal sequence, we obtain the explicit expressions of the ruin probability, the finite-horizon ruin probability, the joint distributions of T, U（T - 1）, ｜U（T）｜ and inf U（n） （i.e., the time of ruin, the surplus immediately before ruin, the deficit at ruin and maximal deficit from ruin to recovery） and the distributions of some actuarial random vectors.