Some solvable stochastic control problemst<sup>†</sup>

Beneš, V. E.; Shepp, Larry; Witsenhausen, H. S.

doi:10.1080/17442508008833156

Cited by 303 publications

(163 citation statements)

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“…A natural and rigorous formulation of this problem is a reflected diffusion process, in which the local times of the diffusion at the boundary provide the trading policy. Similar problems have been studied in [1] and [3].…”

Section: Control Limit Policiesmentioning

confidence: 83%

See 1 more Smart Citation

Portfolio Selection with Transaction Costs

Davis

Norman²

1990

Mathematics of OR

1,157

811

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This thesis considers an investor who can distribute wealth between two assets , one with deterministic rate of growth (eg. bank deposit account) , the other with growth governed by a Brownian motion with drift (eg. equity share) . Transfers between these holdings incur proportional transaction costs . The investor may consume continuously and costlessly from the bank , and requires a consumption and investment strategy which maximises total discounted utility of consumption over an infinite horizon .For a large class of utility functions , it is proved that maximum utility is achieved by a strategy-which confines the investor's portfolio to a certain wedge-shaped region in the portfolio plane, by minimal trading, and allows consumption at a rate depending at any time on the current state of the portfolio .Moreover it is shown that the optimal strategy does not lead to bankruptcy in finite time.The problem is treated rigorously as a reflected diffusion process, and the existence and uniqueness of the optimally-controlled wealth process are demonstrated.

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Section: Control Limit Policiesmentioning

confidence: 83%

“…For a specified utility function u(c) , an optimal (admissible) policy ( Tr,Z ) is then sought, to 7 ra-r1217-1 w1, and the optimal consumption/investment policy 1-7 1-7 2(1_1)2L a J is given by : qt)=P(4V(t)) 1 1/(1-7) = i…”

Section: (Iii) W(t)v T Asmentioning

confidence: 99%

Portfolio Selection with Transaction Costs

Davis

Norman²

1990

Mathematics of OR

1,157

811

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“…The admissibility condition (8) and (53) imply that the random variable on the righthand side of these inequalities has finite expectation. Combining this observation with (51), we can see that E inf T ≥0 M T > −∞.…”

Section: Theorem 1 Suppose That Assumption 1 Holds True the Value Fumentioning

confidence: 99%

“…In their seminal paper, Beneš, Shepp and Witsenhausen [8] were the first to solve rigorously an example of a finite-fuel singular control problem. Since then, the area has attracted considerable interest in the literature.…”

Section: Introductionmentioning

confidence: 99%

Irreversible Capital Accumulation with Economic Impact

Motairi

Zervos

2016

Appl Math Optim

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We consider an irreversible capacity expansion model in which additional investment has a strictly negative effect on the value of an underlying stochastic economic indicator. The associated optimisation problem takes the form of a singular stochastic control problem that admits an explicit solution. A special characteristic of this stochastic control problem is that changes of the state process due to control action depend on the state process itself in a proportional way.

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“…Previous work Singular control problems have been studied extensively in both the mathematics and economics, starting from the well-known monotone fuel follower problem, for which explicit solutions can be found in Bather and Chernoff (1967a,b); Beneš et al (1980); Karatzas (1983) and Harrison and Taksar (1983). In mathematical economics, a typical (ir)reversible investment problem can be formulated as a singular control problem in which a company, by adjusting its production capacity through expansion and contraction according to market fluctuations, wishes to maximize its overall expected net profit over an infinite horizon.…”

Section: Introductionmentioning

confidence: 99%