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1.
In the classical Cram\'{e}r-Lundberg model in risk theory the problem of finding the optimal dividend strategy and optimal dividend return function is a widely discussed topic. In the present paper, we discuss the problem of maximizing the expected discounted net dividend payments minus the expected discounted costs of injecting new capital, in the Cram\'{e}r-Lundberg model with proportional taxes and fixed transaction costs imposed each time the dividend is paid out and with both fixed and proportional transaction costs incurred each time the capital injection is made. Negative surplus or ruin is not allowed. By solving the corresponding quasi-variational inequality, we obtain the analytical solution of the optimal return function and the optimal joint dividend and capital injection strategy when claims are exponentially distributed. 相似文献
2.
??In this paper, we consider the optimal dividend problem in the spectrally positive L\'{e}vy model with regime switching. By an auxiliary optimal problem, the principle of dynamic programming and the fluctuation theory of L\'{e}vy processes, we show that optimal strategy is a modulated barrier strategy. The value function and the optimal dividend barrier are obtained by iteration. 相似文献
3.
In this paper, we study the optimal dividend
problem in a dual risk model, which might be appropriate for
companies that have fixed expenses and occasional profits. Assuming
that dividend payments are subject to both proportional and fixed
transaction costs, our object is to maximize the expected present
value of dividend payments until ruin, which is defined as the first
time the company's surplus becomes negative. This optimization
problem is formulated as a stochastic impulse control problem. By
solving the corresponding quasi-variational inequality (QVI), we
obtain the analytical solutions of the value function and its
corresponding optimal dividend strategy when jump sizes are
exponentially distributed. 相似文献
4.
Stefan Thonhauser 《Insurance: Mathematics and Economics》2007,41(1):163-184
In the Cramér-Lundberg model and its diffusion approximation, it is a classical problem to find the optimal dividend payment strategy that maximizes the expected value of the discounted dividend payments until ruin. One often raised disadvantage of this approach is the fact that such a strategy does not take the lifetime of the controlled process into account. In this paper we introduce a value function which considers both expected dividends and the time value of ruin. For both the diffusion model and the Cramér-Lundberg model with exponential claim sizes, the problem is solved and in either case the optimal strategy is identified, which for unbounded dividend intensity is a barrier strategy and for bounded dividend intensity is of threshold type. 相似文献
5.
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. 相似文献
6.
����³�� ����Ԫ 《应用概率统计》2016,32(4):376-392
For a financial or insurance entity, the problem of finding the
optimal dividend distribution strategy and optimal firm value function is a widely discussed
topic. In the present paper, it is assumed that the firm faces two types of liquidity risks:
a Brownian risk and a Poisson risk. The firm can control the time and amount of dividends
paid out to shareholders. By sufficiently taking into account the safety of the company,
bankruptcy is said to take place at time $t$ if the cash reserve of the firm runs below
the linear barrier b+kt (not zero), see 1. We deal with the problem of maximizing
the expected total discounted dividends paid out until bankruptcy. The optimal dividend
return (or, firm value) function is identified as the classical solution of the associated
Hamilton-Jacobi-Bellman (HJB) equation where a second-order differential-integro equation
is involved. By solving the corresponding HJB equation, the analytical solution of the
optimal firm value function is obtained, the optimal dividend strategy is also characterized,
which is of linear barrier type: at time t the firm keeps cash inside when the cash
reserves level is less than a critical linear barrier and pays cash in excess of
this linear barrier as dividends. 相似文献
7.
We study the optimal reinsurance policy and dividend distribution of an insurance company under excess of loss reinsurance. The objective of the insurer is to maximize the expected discounted dividends. We suppose that in the absence of dividend distribution, the reserve process of the insurance company follows a compound Poisson process. We first prove existence and uniqueness results for this optimization problem by using singular stochastic control methods and the theory of viscosity solutions. We then compute the optimal strategy of reinsurance, the optimal dividend strategy and the value function by solving the associated integro-differential Hamilton–Jacobi–Bellman Variational Inequality numerically. 相似文献
8.
We consider the optimal dividend problem for the insurance risk process in a general Lévy process setting. The objective is to find a strategy which maximizes the expected total discounted dividends until the time of ruin. We give sufficient conditions under which the optimal strategy is of barrier type. In particular, we show that if the Lévy density is a completely monotone function, then the optimal dividend strategy is a barrier strategy. This approach was inspired by the work of Avram et al. [F. Avram, Z. Palmowski, M.R. Pistorius, On the optimal dividend problem for a spectrally negative Lévy process, The Annals of Applied Probability 17 (2007) 156–180], Loeffen [R. Loeffen, On optimality of the barrier strategy in De Finetti’s dividend problem for spectrally negative Lévy processes, The Annals of Applied Probability 18 (2008) 1669–1680] and Kyprianou et al. [A.E. Kyprianou, V. Rivero, R. Song, Convexity and smoothness of scale functions with applications to De Finetti’s control problem, Journal of Theoretical Probability 23 (2010) 547–564] in which the same problem was considered under the spectrally negative Lévy processes setting. 相似文献
9.
We consider the compound binomial model in a Markovian environment presented by Cossette et al.(2004). We modify the model via assuming that the company receives interest on the surplus and a positive real-valued premium per unit time, and introducing a control strategy of periodic dividend payments. A Markov decision problem arises and the control objective is to maximize the cumulative expected discounted dividends paid to the shareholders until ruin minus a discounted penalty for ruin. We show that under the absence of a ceiling of dividend rates the optimal strategy is a conditional band strategy given the current state of the environment process. Under the presence of a ceiling for dividend rates, the character of the optimal control strategy is given. In addition, we offer an algorithm for the optimal strategy and the optimal value function.Numerical results are provided to illustrate the algorithm and the impact of the penalty. 相似文献
10.
Jiaqin Wei Hailiang Yang Rongming Wang 《Journal of Optimization Theory and Applications》2010,147(2):358-377
We consider the optimal proportional reinsurance and dividend strategy. The surplus process is modeled by the classical compound
Poisson risk model with regime switching. Considering a class of utility functions, the object of the insurer is to select
the reinsurance and dividend strategy that maximizes the expected total discounted utility of the shareholders until ruin.
By adapting the techniques and methods of stochastic control, we study the quasi-variational inequality for this classical
and impulse control problem and establish a verification theorem. We show that the optimal value function is characterized
as the unique viscosity solution of the corresponding quasi-variational inequality. 相似文献
11.
In this paper, we consider the optimal dividend problem for the compound Poisson risk model. We assume that dividends are paid to the shareholders according to an admissible strategy with dividend rate bounded by a constant. Our objective is to find a dividend policy so as to maximize the expected discounted value of dividends until ruin. We give sufficient conditions under which the optimal strategy is of threshold type. 相似文献
12.
13.
研究复合二项对偶模型的最优分红问题,通过分析HJB方程得到了最优分红策略和相应的最优值函数之间的关系以及最优值函数的简单计算方法.通过讨论最优红利策略的一些性质得到了最优值函数的可无限逼近的上界和下界. 相似文献
14.
《Operations Research Letters》2020,48(2):170-175
Belhaj (2010) established that a barrier strategy is optimal for the dividend problem under jump–diffusion model. However, if the optimal dividend barrier level is set too low, then the bankruptcy probability may be too high to be acceptable. This paper aims to address this issue by taking the solvency constrain into consideration. Precisely, we consider a dividend payment problem with solvency constraint under a jump–diffusion model. Using stochastic control and PIDE, we derive the optimal dividend strategy of the problem. 相似文献
15.
Consider the optimal dividend problem for an insurance company whose uncontrolled surplus precess evolves as a spectrally negative Levy process. We assume that dividends are paid to the shareholders according to admissible strategies whose dividend rate is bounded by a constant. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. In this paper, we show that a threshold strategy (also called refraction strategy) forms an optimal strategy under the condition that the Levy measure has a completely monotone density. 相似文献
16.
In the classical Cramér–Lundberg model in risk theory the problem of maximizing the expected cumulated discounted dividend payments until ruin is a widely discussed topic. In the most general case within that framework it is proved [Gerber, H.U., 1968. Entscheidungskriterien fuer den zusammengesetzten Poisson-prozess. Schweiz. Aktuarver. Mitt. 1, 185–227; Azcue, P., Muler, N., 2005. Optimal reinsurance and dividend distribution policies in the Cramér–Lundberg model. Math. Finance 15 (2) 261–308; Schmidli, H., 2008. Stochastic Control in Insurance. Springer] that the optimal dividend strategy is of band type. In the present paper we discuss this maximization problem in a generalized setting including a constant force of interest in the risk model. The value function is identified in the set of viscosity solutions of the associated Hamilton–Jacobi–Bellman equation and the optimal dividend strategy in this risk model with interest is derived, which in the general case is again of band type and for exponential claim sizes collapses to a barrier strategy. Finally, an example is constructed for Erlang(2)-claim sizes, in which the bands for the optimal strategy are explicitly calculated. 相似文献
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19.
Natalie Kulenko 《Insurance: Mathematics and Economics》2008,43(2):270-278
We consider a classical risk model with dividend payments and capital injections. Thereby, the surplus has to stay positive. Like in the classical de Finetti problem, we want to maximise the discounted dividend payments minus the penalised discounted capital injections. We derive the Hamilton-Jacobi-Bellman equation for the problem and show that the optimal strategy is a barrier strategy. We explicitly characterise when the optimal barrier is at 0 and find the solution for exponentially distributed claim sizes. 相似文献
20.
In this paper, we study the optimal dividend and capital injection problem with the penalty payment at ruin. The dividend strategy is assumed to be restricted to a small class of absolutely continuous strategies with bounded dividend density. By considering the surplus process killed at the time of ruin, we transform the problem to a combined stochastic and impulse control one up to ruin with a free boundary at zero. We illustrate the theoretical verifications for different types of capital injection strategies comparing to the conventional results given in the literature, where the capital injections are made before the time of ruin. Under the assumption of restricted dividend density, the value function is proved as the unique increasing, bounded, Lipschitz continuous and upper semi-continuous at zero viscosity solution to the corresponding quasi-variational Hamilton–Jacobi–Bellman (HJB) equation. The uniqueness of such class of viscosity solutions is shown by considering its boundary condition at infinity. The optimality of a specific band-type strategy is proved for the case when the premium rate is (i) greater than or (ii) less than the ceiling dividend rate respectively. Some numerical examples are presented under the exponential and gamma claim size assumptions. 相似文献