Optimal Dividend Policy when Cash Reserves Follow a Jump-Diffusion Process Under Markov-Regime Switching

Jiang, Zhengjun

doi:10.1017/s0021900200012298

Cited by 5 publications

(6 citation statements)

References 25 publications

(27 reference statements)

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“…While the literature on optimal stopping problems under regime switching is relatively rich (see, e.g., [4], [7], [16], [17], [35], among others), that on singular stochastic control problems with regime switching is still limited. We refer, e.g., to [25], [26], [32] and [37] where the optimal dividend problem of actuarial science is formulated as a one-dimensional problem under Markov regime switching. If we then further restrict our attention to singular stochastic control problems with a two-dimensional state space and regime shifts, to the best of our knowledge [18] is the only other paper available in the literature.…”

Section: Introductionmentioning

confidence: 99%

On an optimal extraction problem with regime switching

Ferrari

Yang

2018

Adv. Appl. Probab.

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This paper studies a finite-fuel two-dimensional degenerate singular stochastic control problem under regime switching that is motivated by the optimal irreversible extraction problem of an exhaustible commodity. A company extracts a natural resource from a reserve with finite capacity, and sells it in the market at a spot price that evolves according to a Brownian motion with volatility modulated by a two-state Markov chain. In this setting, the company aims at finding the extraction rule that maximizes its expected discounted cash flow, net of the costs of extraction and maintenance of the reserve. We provide expressions both for the value function and for the optimal control. On the one hand, if the running cost for the maintenance of the reserve is a convex function of the reserve level, the optimal extraction rule prescribes a Skorokhod reflection of the (optimally) controlled state process at a certain state and price dependent threshold. On the other hand, in presence of a concave running cost function it is optimal to instantaneously deplete the reserve at the time at which the commodity's price exceeds an endogenously determined critical level. In both cases, the threshold triggering the optimal control is given in terms of the optimal stopping boundary of an auxiliary family of perpetual optimal selling problems with regime switching.

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Section: Introductionmentioning

confidence: 99%

On an optimal extraction problem with regime switching

Ferrari

Yang

2018

Adv. Appl. Probab.

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“…In a discrete-time setting, the analysis is typically considered in the context of risk models for insurance companies (see, e.g., [42] and the more recent [41]). In continuous-time we find, e.g., [1] and [25] where the wealth process is a drifted Brownian motion and the interest rate is modulated by a continuous-time Markov chain (more recently [26] extends [25] to the case of a jumpdiffusive surplus process). Fixed-point methods are adopted in [25] and [26], whereas dynamic programming ideas appear in [1].…”

Section: Methodology and Resultsmentioning

confidence: 89%

Optimal Dividend Payout under Stochastic Discounting

Bandini¹,

Angelis²,

Ferrari³

et al. 2020

Preprint

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Adopting a probabilistic approach we determine the optimal dividend payout policy of a firm whose surplus process follows a controlled arithmetic Brownian motion and whose cash-flows are discounted at a stochastic dynamic rate. Dividends can be paid to shareholders at unrestricted rates so that the problem is cast as one of singular stochastic control. The stochastic interest rate is modelled by a Cox-Ingersoll-Ross (CIR) process and the firm's objective is to maximize the total expected flow of discounted dividends until a possible insolvency time.We find an optimal dividend payout policy which is such that the surplus process is kept below an endogenously determined stochastic threshold expressed as a decreasing function r → b(r) of the current interest rate value. We also prove that the value function of the singular control problem solves a variational inequality associated to a second-order, non-degenerate elliptic operator, with a gradient constraint.

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“…In a discrete-time setting, the analysis is typically considered in the context of risk models for insurance companies (see, e.g., Xie and Zou (2010) and the more recent Tan et al (2015)). In continuous-time we find, for example, Akyildirim et al (2014) and Jiang and Pistorius (2012) where the wealth process is a drifted Brownian motion and the interest rate is modulated by a continuous-time Markov chain (more recently Jiang (2015) extends Jiang and Pistorius (2012) to the case of a jump-diffusive surplus process). Fixed-point methods are adopted in Jiang and Pistorius (2012) and Jiang (2015), whereas dynamic programing ideas appear in Akyildirim et al (2014).…”

Section: Related Literaturementioning

confidence: 92%

Optimal dividend payout under stochastic discounting

Bandini

Angelis

Ferrari

et al. 2022

Mathematical Finance

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Adopting a probabilistic approach we determine the optimal dividend payout policy of a firm whose surplus process follows a controlled arithmetic Brownian motion and whose cash-flows are discounted at a stochastic dynamic rate. Dividends can be paid to shareholders at unrestricted rates so that the problem is cast as one of singular stochastic control. The stochastic interest rate is modeled by a Cox-Ingersoll-Ross (CIR) process and the firm's objective is to maximize the total expected flow of discounted dividends until a possible insolvency time. We find an optimal dividend payout policy which is such that the surplus process is kept below an endogenously determined stochastic threshold expressed as a decreasing continuous function 𝑟 ↦ 𝑏(𝑟) of the current interest rate value. We also prove that the value function of the singular control problem solves a variational inequality associated to a second-order, non-degenerate elliptic operator, with a gradient constraint.

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Optimal Dividend Policy when Cash Reserves Follow a Jump-Diffusion Process Under Markov-Regime Switching

Cited by 5 publications

References 25 publications

On an optimal extraction problem with regime switching

On an optimal extraction problem with regime switching

Optimal Dividend Payout under Stochastic Discounting

Optimal dividend payout under stochastic discounting

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