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.

Hyper-exponential jump-diffusion model under the barrier dividend strategy

In this paper, we consider a hyper-exponential jump-diffusion model with a constant dividend barrier. Explicit solutions for the Laplace transform of the ruin time, and the Gerber- Shiu function are obtained via martingale stopping.

ON DE FINETTI'S OPTIMAL IMPULSE DIVIDEND CONTROL PROBLEM UNDER CHAPTER 11 BANKRUPTCY

Motivated by recent advances made in the study of dividend control and risk management problems involving the U.S.bankruptcy code,in this paper we follow[44]to revisit the De Finetti dividend control problem under the reorganization process and the regulator's intervention documented in U.S.Chapter 11 bankruptcy.We do this by further accommodating the fixed transaction costs on dividends to imitate the real-world procedure of dividend payments.Incorporating the fixed transaction costs transforms the targeting optimal dividend problem into an impulse control problem rather than a singular control problem,and hence computations and proofs that are distinct from[44]are needed.To account for the financial stress that is due to the more subtle concept of Chapter 11 bankruptcy,the surplus process after dividends is driven by a piece-wise spectrally negative Lévy process with endogenous regime switching.Some explicit expressions of the expected net present values under a double barrier dividend strategy,new to the literature,are established in terms of scale functions.With the help of these expressions,we are able to characterize the optimal strategy among the set of admissible double barrier dividend strategies.When the tail of the Lévy measure is log-convex,this optimal double barrier dividend strategy is then verified as the optimal dividend strategy,solving our optimal impulse control problem.

Differentiability of dividends function on jump-diffusion risk process with a barrier dividend strategy

We consider a dividends model with a stochastic jump perturbed by diffusion. First, we prove that the expected discounted dividends function is twice continuously differentiable under the condition that the claim distribution function has continuous density. Then we show that the expected discounted dividends function under a barrier strategy satisfies some integro-differential equation of defective renewal type, and the solution of which can be explicitly expressed as a convolution formula. Finally, we study the Laplace transform of ruin time on the modified surplus process.

Constant Barrier Strategies in a Two-state Markov-modulated Dual Risk Model

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.

China＇s Sponge City construction： A discussion on technical approaches

Since 2014, China has been implementing the Sponge City Construction initiative, which represents an enormous and unprecedented effort by any government in the world for achieving urban sustainability. According to preliminary estimates, the total investment on the Sponge City Plan is roughly 100 to 150 million Yuan （RMB） （$15 to $22.5 million） average per square kilometer or 10 Trillion Yuan （RMB） （$1.5 Trillion） for the 657 cities nationwide. The Sponge City Plan （SCP） calls for the use of natural processes such as soil and vegetation as part of the urban runoff control strategy, which is similar to that of low impact development （LID） and green infrastructure （G1） practices being promoted in many parts of the world. The SCP includes as its goals not only effective urban flood control, but also rainwater harvest, water quality improvement and ecological restoration. So far, the SCP implementation has encountered-some barriers and challenges due to many factors. The present paper presents a review of those barriers and challenges, oftizrs discussions and recommendations on several technical aspects such as control goals and objectives; planning/design and construction of LID/GI practices; performance evaluation. Several key recommendations are proposed on Sponge City implementation strategy, Site-specific regulatory fi＇amework and technical gmdance, Product innovation and certification, LID/GI Project financing, LID/G1 profcssional training and certification, public outreach and education. It is expected that the successful implemen!atiun of the. SCP not only will bring about a sustainable, eco-friendly urbanization process in China, but also contribute enormously to the LID/Gl research and development with the vast amount of relevant data and experiences generated from the Sponge City construction projects.

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.

A Note on Moments of Dividends

We reconsider a formula for arbitrary moments of expected discounted dividend payments in a spectrally negative Lévy risk model that was obtained in Renaud and Zhou （2007, [4]） and in Kyprianou and Palmowski （2007, [3]） and extend the result to stationary Markov processes that are skip-free upwards.