Optimal Stopping Problems in Lévy Models with Random Observations

Boyarchenko, Svetlana; Levendorskiı̌, Sergei

doi:10.1007/s10440-018-0212-z

Cited by 1 publication

(2 citation statements)

References 41 publications

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“…26 This partial observation framework leads to a control problem subject to discrete and random observations that has been used in some financial models under restricted observation chances. [27][28][29] Another difference between the ideal and real problems is the execution delay. Interventions that have much shorter time-scales than those of the target dynamics are reasonably considered to be impulsive.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic impulse control of nonsmooth dynamics with partial observation and execution delay: Application to an environmental restoration problem

Yoshioka

Yaegashi²

2021

Optim Control Appl Methods

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Nonsmooth dynamics driven by stochastic disturbance arise in a wide variety of engineering problems. Impulsive interventions are often employed to control stochastic systems; however, the modeling and analysis subject to execution delay have been less explored. In addition, continuously receiving information of the dynamics is not always possible. In this article, with an application to an environmental restoration problem, a continuous-time stochastic impulse control problem subject to execution delay under discrete and random observations is newly formulated and analyzed. The dynamics have a nonsmooth coefficient modulated by a Markov chain, and eventually attain an undesirable state like a depletion due to the nonsmoothness. The goal of the control problem is to find the most cost-efficient policy that can prevent the dynamics from attaining the undesirable state. We demonstrate that finding the optimal policy reduces to solving a nonstandard system of degenerate elliptic equations, the Hamilton-Jacobi-Bellman equation (HJBE), which is rigorously and analytically verified in a simplified case. The associated Fokker-Planck equation (FPE) for the controlled dynamics is derived and solved explicitly as well. The model is finally applied to numerical computation of a recent river environmental restoration problem. The HJBE and FPE are successfully computed, and the optimal policy and the probability density functions are numerically obtained.The impacts of execution delay are discussed to deeper analyze the model.

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Section: Introductionmentioning

confidence: 99%

“…In some models, even the assumption of the scheduled observations is relaxed and only random observation processes are assumed [26]. This partial observation framework leads to a control problem subject to discrete and random observations that has been used in some financial models under restricted observation chances [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Stochastic impulse control of nonsmooth dynamics with partial observation and execution delay: Application to an environmental restoration problem

Yoshioka

Yaegashi²

2021

Optim Control Appl Methods

View full text Add to dashboard Cite

show abstract

Optimal Stopping Problems in Lévy Models with Random Observations

Cited by 1 publication

References 41 publications

Stochastic impulse control of nonsmooth dynamics with partial observation and execution delay: Application to an environmental restoration problem

Stochastic impulse control of nonsmooth dynamics with partial observation and execution delay: Application to an environmental restoration problem

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