Singular stochastic control and optimal stopping

Baldursson, Fridrik M.

doi:10.1080/17442508708833449

Cited by 24 publications

(20 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The articles [5], [15], and [16] consider the case of Brownian motion with an added bounded variation control process. The work of [5] considers the case of a diffusion process and their drift and diffusion coefficients are allowed to be time dependent, but the drift term is linear and the diffusion is independent of the space variable. The running cost function is a symmetric convex function in [5], [13], [15], and [16].…”

Section: Introductionmentioning

confidence: 99%

“…Here we employ the connection between stochastic control and optimal stopping, which is a known theme in optimal control theory. We refer to [3], [4], [5], [7], [15], [16], [27], and [35] for this approach. The articles [5], [15], and [16] consider the case of Brownian motion with an added bounded variation control process.…”

Section: Introductionmentioning

confidence: 99%

“…We refer to [3], [4], [5], [7], [15], [16], [27], and [35] for this approach. The articles [5], [15], and [16] consider the case of Brownian motion with an added bounded variation control process. The work of [5] considers the case of a diffusion process and their drift and diffusion coefficients are allowed to be time dependent, but the drift term is linear and the diffusion is independent of the space variable.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Bounded Variation Control Problem for Diffusion Processes

Weerasinghe

2005

SIAM J. Control Optim.

View full text Add to dashboard Cite

We consider an infinite horizon discounted cost minimization problem for a onedimensional stochastic differential equation model. The available control is an added bounded variation process. The cost structure involves a running cost function and a proportional cost for the use of the control process. The running cost function is not necessarily convex. We obtain sufficient conditions to guarantee the optimality of the zero control. Also, for unbounded cost functions, we provide sufficient conditions which make our optimal state process a reflecting diffusion on a compact interval. In both cases, the value function is a C 2 function. For bounded cost functions, under additional assumptions, we obtain a complex optimal strategy which turned out to be a mixture of jumps and local-time-type processes. In this case, we show that the value function is only a C 1 function and that it fails to be a C 2 function. We also discuss a related variance control problem.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Bounded Variation Control Problem for Diffusion Processes

Weerasinghe

2005

SIAM J. Control Optim.

View full text Add to dashboard Cite

show abstract

“…This connection dates back to Bather and Chernoff [4] and has led to many generalizations and an extensive literature; see [2] and [3] and the references therein. The optimal stopping problem (5.3) is not of the form (2.1) because the payoff has to be integrated over time up to τ , instead of at the stopping time τ .…”

Section: Boundary Correction In Singular Stochastic Controlmentioning

confidence: 99%

“…over bounded variation processes {ξ t } that are adapted to the filtration generated by a standard Brownian motion {B t } such that X t = x + B t + ξ t ; see [2] and [3]. In (5.1) the functions h, f , and k respectively represent the deviation of X t from 0, the unit cost of effort ξ t , and the terminal penalty when the state is away from the target state 0.…”

Section: Boundary Correction In Singular Stochastic Controlmentioning

confidence: 99%