In the dual risk model, we consider the optimal dividend and capital injection problem, which involves a random time horizon and a ruin penalty. Both fixed and proportional costs from the transactions of capital injec...In the dual risk model, we consider the optimal dividend and capital injection problem, which involves a random time horizon and a ruin penalty. Both fixed and proportional costs from the transactions of capital injection are considered. The objective is to maximize the total value of the expected discounted dividends, and the penalized discounted both capital injections and ruin penalty during the horizon, which is described by the minimum of the time of ruin and an exponential random variable. The explicit solutions for optimal strategy and value function are obtained, when the income jumps follow a hyper-exponential distribution.Besides, some numerical examples are presented to illustrate our results.展开更多
The spectrally negative Lévy risk model with random observation times is considered in this paper,in which both dividends and capital injections are made at some independent Poisson observation times.Under the ab...The spectrally negative Lévy risk model with random observation times is considered in this paper,in which both dividends and capital injections are made at some independent Poisson observation times.Under the absolute ruin,the expected discounted dividends and the expected discounted capital injections are discussed.We also study the joint Laplace transforms including the absolute ruin time and the total dividends or the total capital injections.All the results are expressed in scale functions.展开更多
We consider an optimization problem of an insurance company in the diffusion setting, which controls the dividends payout as well as the capital injections. To maximize the cumulative expected discounted dividends min...We consider an optimization problem of an insurance company in the diffusion setting, which controls the dividends payout as well as the capital injections. To maximize the cumulative expected discounted dividends minus the penalized discounted capital injections until the ruin time, there is a possibility of （cheap or non-cheap） proportional reinsurance. We solve the control problems by constructing two categories of suboptimal models, one without capital injections and one with no bankruptcy by capital injection. Then we derive the explicit solutions for the value function and totally characterize the optimal strategies. Particularly, for cheap reinsurance, they axe the same as those in the model of no bankruptcy.展开更多
This work focuses on numerical methods for finding optimal dividend payment and capital injection policies to maximize the present value of the difference between the cumulative dividend payment and the possible capit...This work focuses on numerical methods for finding optimal dividend payment and capital injection policies to maximize the present value of the difference between the cumulative dividend payment and the possible capital injections. Using dynamic programming principle, the value function obeys a quasi-variational inequality （QVI）. The state constraint of the impulsive control gives rise to a capital injection region with free boundary. Since the closed-form solutions are virtually impossible to obtain, we use Markov chain approximation techniques to construct a discrete-time controlled Markov chain to approximate the value function and optimal controls. Convergence of the approximation algorithms is proved.展开更多
基金Supported by the National Natural Science Foundation of China(11231005)Promotive research fund for excellent young and middle-aged scientists of Shandong Province(BS2014SF006)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(15KJB110009)
文摘In the dual risk model, we consider the optimal dividend and capital injection problem, which involves a random time horizon and a ruin penalty. Both fixed and proportional costs from the transactions of capital injection are considered. The objective is to maximize the total value of the expected discounted dividends, and the penalized discounted both capital injections and ruin penalty during the horizon, which is described by the minimum of the time of ruin and an exponential random variable. The explicit solutions for optimal strategy and value function are obtained, when the income jumps follow a hyper-exponential distribution.Besides, some numerical examples are presented to illustrate our results.
基金Supported by the National Natural Science Foundation of China(11701319,11571198).
文摘The spectrally negative Lévy risk model with random observation times is considered in this paper,in which both dividends and capital injections are made at some independent Poisson observation times.Under the absolute ruin,the expected discounted dividends and the expected discounted capital injections are discussed.We also study the joint Laplace transforms including the absolute ruin time and the total dividends or the total capital injections.All the results are expressed in scale functions.
基金Supported by the National Basic Research Program of China (973 Program) (Grant No. 2007CB814905)the National Natural Science Foundation of China (NSFC Grant No. 10871102)
文摘We consider an optimization problem of an insurance company in the diffusion setting, which controls the dividends payout as well as the capital injections. To maximize the cumulative expected discounted dividends minus the penalized discounted capital injections until the ruin time, there is a possibility of （cheap or non-cheap） proportional reinsurance. We solve the control problems by constructing two categories of suboptimal models, one without capital injections and one with no bankruptcy by capital injection. Then we derive the explicit solutions for the value function and totally characterize the optimal strategies. Particularly, for cheap reinsurance, they axe the same as those in the model of no bankruptcy.
基金supported in part by Early Career Research Grant and Faculty Research Grant by The University of Melbournesupported in part by Research Grants Council of the Hong Kong Special Administrative Region(project No.HKU 17330816)+1 种基金Society of Actuaries’Centers of Actuarial Excellence Research Grantsupported in part by U.S.Army Research Office under grant W911NF-15-1-0218
文摘This work focuses on numerical methods for finding optimal dividend payment and capital injection policies to maximize the present value of the difference between the cumulative dividend payment and the possible capital injections. Using dynamic programming principle, the value function obeys a quasi-variational inequality （QVI）. The state constraint of the impulsive control gives rise to a capital injection region with free boundary. Since the closed-form solutions are virtually impossible to obtain, we use Markov chain approximation techniques to construct a discrete-time controlled Markov chain to approximate the value function and optimal controls. Convergence of the approximation algorithms is proved.
