Advanced search
Publication Cover
Stochastics
An International Journal of Probability and Stochastic Processes
Volume 89, 2017 - Issue 6-7: Proceedings of the Hammamet Conference, 19-23 October 2015
Submit an article Journal homepage
63
Views
0
CrossRef citations to date
0
Altmetric
Articles

Infinite horizon impulse control problem with continuous costs, numerical solutions

Hani AbidiFaculty of Sciences of Tunis, Department of Mathematics, University of Tunis El Manar, Tunis, Tunisia.Correspondence[email protected]
,
Rim AmamiFaculty of Sciences of Tunis, Department of Mathematics, University of Tunis El Manar, Tunis, Tunisia.
&
Monique PontierDepartement de Mathématiques, Institut Mathématique de Toulouse, Toulouse, France.
Pages 1039-1060 | Received 30 Mar 2016, Accepted 14 Mar 2017, Published online: 10 Apr 2017

References

  • R. Amami, Application of doubly reflected BSDEs to an impulse control problem, Optim.: A J. Math. Program. Oper. Res. 62(11) (2013), pp. 1525–1552.
  • E. Bayraktar and M. Egami, On the one-dimensional optimal switching problem. Math. Oper. Res. 35(1) (2010), pp. 140–159.
  • B. Bouchard and J.F. Chassagneux, Discrete-time approximation for continuously and discretely reflected BSDEs, Stochastic Process. Appl. 118(12) (2008), pp. 2269–2293.
  • B. Bouchard and N. Touzi, Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations, Stochastic Process. Appl. 111(2) (2004), pp. 175–206.
  • J.F. Chassagneux, Discrete-time approximation of doubly reflected BSDE’s, Adv. Appl. Probab. 41(1) (2009), pp. 101–130.
  • J. Cvitanic and I. Karatzas, Backward stochastic differential equations with reflection and Dynkin games, Ann. Probab. 24(4) (1996), pp. 2024–2056.
  • N. El Karoui, Les Aspects Probabilistes du Contrôle Stochastique [Probabilistic Aspects of Stochastic Control], Lecture Notes in Mathematics Vol. 876, Springer-Verlag, Berlin, 1981.
  • P.E. Kloeden and E. Platen, Numerical Solutions of Stochastic Differential Equations, Applied of Mathematics Vol. 23, Springer, Berlin, 1992.
  • E. Gobet and C. Labart, A regression-based Monte-Carlo method to solve backward stochastic differential equations. 15(3) (2005), pp. 2172–2002.
  • E. Gobet, J.P. Lemor, and X. Warin, Error expansion for the discretization of backward stochastic differential equations. 117(7) (2007), pp. 803–829.
  • E. Gobet and P. Turkedjiev, Linear regression MDP scheme for discrete backward stochastic differential equations under general conditions. Math. Comput. 85 (2016), pp. 1359–1391.
  • S. Hamadène and M. Jeanblanc, On the starting and stopping problem: Application in reversible investments, Math. Oper. Res. 32(1) (2007), pp. 182–192.
  • S. Hamadène, J.P. Lepeltier, and A. Matoussi, Double barrier reflected backward SDEs with continuous coefficient, Pitman Res. Notes Math. Ser. 364 (1997), pp. 115–128.
  • S. Hamadène, J.P. Lepeltier, and Z. Wu, Infinite horizon reflected backward stochastic differential equations and applications in mixed control and game problems, Probab. Math. Stat. 19(2) (1999), pp. 211–234.
  • L. Jiang and M. Dai, Convergence of BTM for European/American path-dependent options, SIAM J. Numer. Anal. 42 (2004), pp. 1094–1109.
  • J. Liang, B. Hu, L. Jian, and B. Bian, On the rate of convergence of the binomial tree scheme for American options, Numer. Math. 107 (2007), pp. 333–352.
  • F. Longstaff and E. Schwartz, Valuing American options by simulation: A simple least-squares, Rev. Financ. Stud. 1(14) (2001), pp. 113–147.
  • E. Pardoux and S.G. Peng, Adapted Solution of a Backward Stochastic Differential Equation. Systems Control lett. 14 (1990), pp. 55–61.
  • E. Pardoux and S.G. Peng, Backward stochastic differential equations and quasilinear Parabolic partial differential equations, in Stochastic Differential Equations and their Applications, Lecture Notes in Control and Information Sciences Vol. 176, B. Rozovskii and R. Sowers, eds., Springer, 1992, pp. 200–217.
  • M. Xu, Numerical algorithms and simulations for reflected backward stochastic differential equations with two continuous barriers, J. Comput. Appl. Math. 236 (2011), pp. 1137–1154.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Supercharge Your Next Research Paper: Research and write your next paper with Jenni AI.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.