Optimal dividend and equity issuance problem with proportional and fixed transaction costs

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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“…Similar to Lemma 3.1 in [11], and by the optimality of the value function V (x), we obtain that V (x) is increasing and satisfies…”

Section: Optimal Control Problemsupporting

confidence: 53%

“…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. Fixed costs on dividend were studied in [4].…”

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

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“…By the optimality of the value function V (x) and similar to Lemma 3.1 in Peng et al (2012), we obtain that V (x) is increasing and satisfies…”

Section: Preliminary Discussion For Optimal Problemmentioning

confidence: 74%

“…Proof of Lemma 2.1. Similar to Lemma 3.2 in Peng et al (2012), we prove the result by constructing a strategyπ such as V (x;π) ≥ V (x; π) where π is an admissible strategy with the amount of capital injections z > 0 at the initial time, i.e., τ π 1 = 0 and ξ π 1 = z. We define the stopping time τ π z = inf{t ≥ 0 : X π t ≤ z} and the number of capital injections before τ π z by m = sup{n ≥ 1 : τ π n < τ π z }.…”

mentioning

confidence: 64%

Optimal periodic dividend and capital injection problem for spectrally positive Lévy processes

Zhao

Chen

Yang

2017

Insurance: Mathematics and Economics

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In this paper, we investigate an optimal periodic dividend and capital injection problem for spectrally positive Lévy processes. We assume that the periodic dividend strategy has exponential inter-dividend-decision times and continuous monitoring of solvency. Both proportional and fixed transaction costs from capital injection are considered. The objective is to maximize the total value of the expected discounted dividends and the penalized discounted capital injections until the time of ruin. By the fluctuation theory of Lévy processes in Albrecher et al. (2016), the optimal periodic dividend and capital injection strategies are derived. We also find that the optimal return function can be expressed in terms of the scale functions of Lévy processes. Finally, numerical examples are studied to illustrate our results.

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“…On the basis of that, we can do the sensitivity analysis of costs on the optimal strategies and the value functions clearly and directly. This method can be used in a general case, such as [4,15,17,22,23], § and some other literature.…”

Section: Problem Formulation and Preliminarymentioning

confidence: 99%

Optimal control problem for an insurance surplus model with debt liability

Wei

Zhou

2013

Math Methods in App Sciences

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For an insurance company with a debt liability, they could make some management actions, such as reinsurance, paying dividends, and capital injection, to balance the profitability and financial bankruptcy. Our objective is to determine risk retention rate, dividend, and capital injection strategy so as to maximize the expected discounted dividends minus the discounted cost of capital injection until the time of ruin. We assume that the dividend payments and capital injection should occur with both fixed and proportional costs. We obtain explicit expressions of the optimal value functions as well as the corresponding optimal joint strategies by routine procedures in a comprehensive basic model using a new technique to solve the related equations. Our results show that whether recapitalizing is profitable or not depends on the costs of capital raising and that the firm injects capital only when the reserves are zero and recapitalizes to the optimal reserves level if the cost of external capital is low. Copyright © 2013 John Wiley & Sons, Ltd.

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Optimal dividend and equity issuance problem with proportional and fixed transaction costs

Cited by 36 publications

References 21 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 periodic dividend and capital injection problem for spectrally positive Lévy processes

Optimal control problem for an insurance surplus model with debt liability

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