In this paper, we consider the dividend problem in a two-state Markov-modulated dual risk model, in which the gain arrivals, gain sizes and expenses are influenced by a Markov process. A system of integro-differential equations for the expected value of the discounted dividends until ruin is derived. In the case of exponential gain sizes, the equations are solved and the best barrier is obtained via numerical example. Finally, using numerical example, we compare the best barrier and the expected discounted dividends in the two-state Markov-modulated dual risk model with those in an associated averaged compound Poisson risk model. Numerical results suggest that one could use the results of the associated averaged compound Poisson risk model to approximate those for the two-state Markov-modulated dual risk model.
In this paper, new risk measures are introduced, tation results are also given. These newly introduced risk introduced by Song and Yan （2009） and Karoui （2009）. and the corresponding represen- measures are extensions of those
By the Cramér method, the large deviation principle for a form of compound Poisson process S(t)=∑N(t)i=1h(t-Si)Xi is obtained,where N(t), t>0, is a nonhomogeneous Poisson process with intensity λ(t)>0, Xi, i≥1, are i.i.d. nonnegative random variables independent of N(t), and h(t), t>0, is a nonnegative monotone real function. Consequently, weak convergence for S(t) is also obtained.
In this paper, we propose a customer-based individual risk model, in which potential claims by customers are described as i.i.d, heavy-tailed random variables, but different insurance policy holders are allowed to have different probabilities to make actual claims. Some precise large deviation results for the prospectiveoss process are derived under certain mild assumptions, with emphasis on the case of heavy-tailed distribution function class ERV （extended regular variation）. Lundberg type limiting results on the finite time ruin probabilities are also investigated.
This paper considers the dividend optimization problem for an insurance company under the consideration of internal competition between different units inside the company. The objective is to find a reinsurance policy and a dividend payment scheme so as to maximize the expected discounted value of the dividend payment, and the expected present value of an amount which the insurer earns until the time of ruin. By solving the corresponding constrained Hamilton-Jacobi-Bellman （HJB） equation, we obtain the value function and the optimal reinsurance policy and dividend payment.
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.
