Optimal financing and dividend strategies in a dual model with proportional costs

Yao, Dingjun; Yang, Hailiang; Wang, Rongming

doi:10.3934/jimo.2010.6.761

Cited by 27 publications

(14 citation statements)

References 16 publications

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“…This idea goes back to [6,7]. In [8,9], Yao et al considered the optimal dividend and capital injection problem in the dual compound Poisson risk model. In [10], Avanzi et al discussed the same problem in the dual compound Poisson model with diffusion.…”

Section: Introductionmentioning

confidence: 98%

“…In addition, transaction cost, which usually includes two partsproportional cost and fixed cost-, is an important factor in business activities. In [8,10], proportional costs on both dividend and capital injection were involved into the optimal dividend problem. In [9,11], both proportional and fixed costs on capital injection were considered.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Dividends and Capital Injections in the Dual Model with a Random Time Horizon

Zhao

Wang

Yao

et al. 2014

J Optim Theory Appl

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This paper investigates an optimal dividend and capital injection problem in the dual model with a random horizon. 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 capital injections during the horizon, which is described by the minimum of the time of ruin and an exponential random variable. By the fluctuation theory of Lévy processes, the optimal dividend and capital injection strategy is obtained. We also find that the optimal return function can be expressed in terms of the scale functions of Lévy processes. Besides, numerical examples are studied to illustrate our results.

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Optimal Dividends and Capital Injections in the Dual Model with a Random Time Horizon

Zhao

Wang

Yao

et al. 2014

J Optim Theory Appl

Self Cite

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show abstract

“…To make the problem more interesting, the issue of capital injections has also been considered in the study of optimal dividends in the dual model. Yao et al [23] studied the optimal problem with dividend payments and issuance of equity in the dual model with proportional transaction costs, and derived the optimal strategy that maximizes the expected present value of dividend payments minus the discounted costs of issuing new equity before ruin. Yao et al [24] considered the same problem with both fixed and proportional transaction costs.…”

Section: Introductionmentioning

confidence: 99%

Optimal dividend problems for a jump-diffusion model with capital injections and proportional transaction costs

Yin¹,

Yuen²

2015

Journal of Industrial &Amp; Management Optimization

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In this paper, we study the optimal control problem for a company whose surplus process evolves as an upward jump diffusion with random return on investment.Three types of practical optimization problems faced by a company that can control its liquid reserves by paying dividends and injecting capital. In the first problem, we consider the classical dividend problem without capital injections. The second problem aims at maximizing the expected discounted dividend payments minus the expected discounted costs of capital injections over strategies with positive surplus at all times. The third problem has the same objective as the second one, but without the constraints on capital injections. Under the assumption of proportional transaction costs, we identify the value function and the optimal strategies for any distribution of gains.

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“…For example, see Albrecher et al [3] for optimal dividend problem, see Cheung and Drekic [4] for dividend approximation and dual risk model with perturbation, see Yao et al [5] for optimal dividend and equity issuance, see Zhu and Yang [6] for ruin probability under a Markov modulated dual risk model.…”

Section: Introductionmentioning

confidence: 99%

Optimal Investment under Dual Risk Model and Markov Modulated Financial Market

Xu¹,

Zhang²,

Zhu

2015

JMF

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In this paper, the optimal investment problem for an agent with dual risk model is studied. The financial market is assumed to be a diffusion process with the coefficients modulated by an external process, which is specified by the solution to a kind of stochastic differential equation. The object of the agent is to maximize the expected utility from terminal wealth. Together with the regularity property of the value function, by dynamic programming principle, the value function of our control problem is turned to be the unique solution to the associated Hamilton-Jacob-Bellman (HJB for short) equation. When the utility is an exponential function with constant risk aversion, close form expressions for value function and optimal investment policy are obtained.

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Optimal financing and dividend strategies in a dual model with proportional costs

Cited by 27 publications

References 16 publications

Optimal Dividends and Capital Injections in the Dual Model with a Random Time Horizon

Optimal Dividends and Capital Injections in the Dual Model with a Random Time Horizon

Optimal dividend problems for a jump-diffusion model with capital injections and proportional transaction costs

Optimal Investment under Dual Risk Model and Markov Modulated Financial Market

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