Jinxia Zhu

Ruin Probabilities of a Dual Markov-Modulated Risk Model

This article is devoted to studying a dual Markov-modulated risk model, which can properly represent, to some extent, surplus processes of companies that pay costs continuously and have occasional gains. We consider both the finite and infnite horizon ruin probabilities under this dual model. Upper and lower bounds of Lundberg type are derived for these ruin probabilities. We also obtain a time-dependent version of Lundberg type inequalities.

Singular optimal dividend control for the regime-switching Cramér-Lundberg model with credit and debit interest

We investigate the dividend optimization problem for a company whose surplus process is modeled by a regime-switching compound Poisson model with credit and debit interest. The surplus process is controlled by subtracting the cumulative dividends. The performance of a dividend distribution strategy which determines the timing and amount of dividend payments, is measured by the expectation of the total discounted dividends until ruin. The objective is to identify an optimal dividend strategy which attains the maximum performance. We show that a regime-switching band strategy is optimal.

Optimal Dividend Control for a Generalized Risk Model with Investment Incomes and Debit Interest

This paper investigates dividend optimization of an insurance corporation under a more realistic model, which takes into consideration refinancing or capital injections. The model follows the compound Poisson framework with credit interest for positive reserve and debit interest for negative reserve. Ruin occurs when the reserve drops below the critical value. The company controls the dividend pay-out dynamically with the objective to maximize the expected total discounted dividends until ruin. We show that the optimal strategy, is a band strategy and it is optimal to pay no dividends when the reserve is negative.

Dividend optimization for general diffusions with restricted dividend payment rates

The dividend optimization problem is studied for a surplus process modeled by a general diffusion where both the drift and diffusion coefficients are functions of the surplus. The dividend payment rate is restricted. The objective is to find an optimal strategy that maximizes the total expected discounted dividends until ruin. It is shown that an optimal strategy is to pay no dividends when the surplus is below a threshold and to pay out dividends at the maximal possible rate when the surplus reaches or is above the threshold . We also give a result on how to determine and the value function and derive some analytical properties of the value function.

Dividend Optimization for Regime Switching General Diffusions

We consider the optimal dividend distribution problem of a financial corporation whose surplus is modeled by a general diffusion process with both the drift and diffusion coefficients depending on the external economic regime as well as the surplus itself through general functions. The aim is to find a dividend payout scheme that maximizes the present value of the total dividends until ruin. We show that, depending on the configuration of the model parameters, there are two exclusive scenarios: (i)the optimal strategy uniquely exists and corresponds to paying out all surpluses in excess of a critical level (barrier) dependent on the economic regime and paying nothing when the surplus is below the critical level;(ii)there are no optimal strategies.

DIVIDEND OPTIMIZATION FOR A REGIME-SWITCHING DIFFUSION MODEL WITH RESTRICTED DIVIDEND RATES

We consider the optimal dividend control problem to find an optimal strategy under the constraint that dividend rates are restricted such that the expected total discounted dividends is maximized for an insurance company. The evolution of the reserve is modeled by a diffusion process with drift and volatility coefficients modulated by an observable Markov chain. We consider the regime-switching threshold strategy, which pays out dividends at the maximal possible rate when the current reserve is above some critical level dependent on the regime of the Markov chain at the time, and to pay nothing when the reserve is below that level. We give sufficient conditions under which such type of strategy is optimal for the regime-switching model.

Optimal financing and dividend distribution in a general diffusion model with regime switching

Abstract We study the optimal financing and dividend distribution problem with restricted dividend rates in a diffusion type surplus model, where the drift and volatility coefficients are general functions of the level of surplus and the external environment regime. The environment regime is modeled by a Markov process. Both capital injection and dividend payments incur expenses. The objective is to maximize the expectation of the total discounted dividends minus the total cost of the capital injection. We prove that it is optimal to inject capital only when the surplus tends to fall below 0 and to pay out dividends at the maximal rate when the surplus is at or above the threshold, dependent on the environment regime.

Ruin Probabilities for the Perturbed Compound Poisson Risk Process with Investment

In this paper, we consider the perturbed compound Poisson risk process with investment incomes. The risk reserve process is perturbed by an independent Brownian motion and the surplus is invested at a constant force of interest. We investigate the asymptotic behavior of the ruin probability as the initial reserve goes to infinity. Bounds and time-dependent bounds are derived the ultimate ruin probability and the probabilities of ruin within finite time, respectively. We also obtain an explicit expression for the Laplace transform of the ultimate ruin probability.

Upper Bounds for the Ruin Probabilities of the Entrance-Based Risk Model

Li et al. (2005) proposed a risk model based on the entrance process and studied the asymptotic behavior of the surplus when time goes to infinity. This article considers the ruin problem in that model. Some simple characteristics (stochastic intensity, compensator, mean process, etc.) of the risk process and other related processes are also considered. Under small claim condition, exponential upper bounds for the ruin probability are obtained.