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An implicit method for the finite time horizon Hamilton–Jacobi–Bellman quasi-variational inequalities

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  • Ieda, Masashi

Abstract

We propose a new numerical method for solving the Hamilton–Jacobi–Bellman quasi-variational inequality associated with the combined impulse and stochastic optimal control problem over a finite time horizon. Our method corresponds to an implicit method in the field of numerical methods for partial differential equations, and thus it is advantageous in the sense that the stability condition is independent of the discretization parameters. We apply our method to the finite time horizon optimal forest harvesting problem, which considers exiting from the forestry business at a finite time. We show that the behavior of the obtained optimal harvesting strategy of the extended problem coincides with our intuition.

Suggested Citation

  • Ieda, Masashi, 2015. "An implicit method for the finite time horizon Hamilton–Jacobi–Bellman quasi-variational inequalities," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 163-175.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:163-175
    DOI: 10.1016/j.amc.2015.04.031
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    1. Ralf Korn, 1999. "Some applications of impulse control in mathematical finance," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(3), pages 493-518, December.
    2. Abel Cadenillas & Fernando Zapatero, 2000. "Classical and Impulse Stochastic Control of the Exchange Rate Using Interest Rates and Reserves," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 141-156, April.
    3. Willassen, Yngve, 1998. "The stochastic rotation problem: A generalization of Faustmann's formula to stochastic forest growth," Journal of Economic Dynamics and Control, Elsevier, vol. 22(4), pages 573-596, April.
    4. Stanley Pliska & Kiyoshi Suzuki, 2004. "Optimal tracking for asset allocation with fixed and proportional transaction costs," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 233-243.
    5. Mundaca, Gabriela & Oksendal, Bernt, 1998. "Optimal stochastic intervention control with application to the exchange rate," Journal of Mathematical Economics, Elsevier, vol. 29(2), pages 225-243, March.
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    Cited by:

    1. Unami, Koichi & Mohawesh, Osama & Fadhil, Rasha M., 2019. "Time periodic optimal policy for operation of a water storage tank using the dynamic programming approach," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 418-431.
    2. Behzad Kafash, 2019. "Approximating the Solution of Stochastic Optimal Control Problems and the Merton’s Portfolio Selection Model," Computational Economics, Springer;Society for Computational Economics, vol. 54(2), pages 763-782, August.

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