Exact Optimal Stopping for Multidimensional Linear Switching Diffusions

Published Online:https://doi.org/10.1287/moor.2022.1312

References

  • [1] Applebaum D (2009) Lévy Processes and Stochastic Calculus (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • [2] Borwein JM, Vanderwerff JD (2010) Convex Functions: Constructions, Characterizations and Counterexamples (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • [3] Christensen S, Crocce F, Mordecki E, Salminen P (2019) On optimal stopping of multidimensional diffusions. Stochastic Processes Appl. 129(7):2561–2581.CrossrefGoogle Scholar
  • [4] Chung KL (2013) Lectures from Markov Processes to Brownian Motion, Grundlehren der Mathematischen Wissenschaften: Comprehensive Studies in Mathematics, vol. 249 (Springer Science & Business Media, New York).Google Scholar
  • [5] Dai S, Menoukeu-Pamen O (2018) Viscosity solution for optimal stopping problems of Feller processes. Preprint, submitted March 10, https://arxiv.org/abs/1803.03832.Google Scholar
  • [6] Dayanik S (2008) Optimal stopping of linear diffusions with random discounting. Math. Oper. Res. 33(3):645–661.LinkGoogle Scholar
  • [7] Dayanik S, Karatzas I (2003) On the optimal stopping problem for one-dimensional diffusions. Stochastic Processes Appl. 107(2):173–212.CrossrefGoogle Scholar
  • [8] De Angelis T, Peskir G (2020) Global C1 regularity of the value function in optimal stopping problems. Ann. Appl. Probab. 30(3):1007–1031.CrossrefGoogle Scholar
  • [9] Du Toit J, Peskir G (2009) Selling a stock at the ultimate maximum. Ann. Appl. Probab. 19(3):983–1014.CrossrefGoogle Scholar
  • [10] Eizenberg A, Freidlin M (1990) On the Dirichlet problem for a class of second order PDE systems with small parameter. Stochastics Stochastic Rep. 33(3-4):111–148.CrossrefGoogle Scholar
  • [11] Ernst PA, Peskir G (2020) Quickest real-time detection of a Brownian coordinate drift. Preprint, submitted July 28, https://arxiv.org/abs/2007.14786.Google Scholar
  • [12] Ferreyra G, Sundar P (2000) Comparison of solutions of stochastic equations and applications. Stochastic Anal. Appl. 18(2):211–229.CrossrefGoogle Scholar
  • [13] Gapeev PV, Shiryaev AN (2013) Bayesian quickest detection problems for some diffusion processes. Adv. Appl. Probab. 45(1):164–185.CrossrefGoogle Scholar
  • [14] Gilbarg D, Trudinger NS (2001) Elliptic Partial Differential Equations of Second Order (Springer, Berlin).CrossrefGoogle Scholar
  • [15] Jobert A, Rogers LCG (2006) Option pricing with Markov-modulated dynamics. SIAM J. Control Optim. 44(6):2063–2078.CrossrefGoogle Scholar
  • [16] Karatzas I, Shreve SE (1998) Brownian Motion and Stochastic Calculus, Graduate Texts in Mathematics (Springer, New York).CrossrefGoogle Scholar
  • [17] Lamberton D, Zervos M (2013) On the optimal stopping of a one-dimensional diffusion. Electronic J. Probab. 18(34):1–49.Google Scholar
  • [18] Liu RH (2016) Optimal stopping of switching diffusions with state dependent switching rates. Stochastics 88(4):586–605.CrossrefGoogle Scholar
  • [19] McKean HP (1965) A free boundary problem for the heat equation arising from a problem of mathematical economics. Indust. Management Rev. 6:32–39.Google Scholar
  • [20] Peskir G (2007) A change-of-variable formula with local time on surfaces. Donati-Martin C, Émery M, Rouault A, Stricker C, eds. Séminaire de Probabilités XL, Lecture Notes in Mathematics, vol. 1899, (Springer, Berlin), 69–96.CrossrefGoogle Scholar
  • [21] Peskir G (2019) Continuity of the optimal stopping boundary for two-dimensional diffusions. Ann. Appl. Probab. 29(1):505–530.CrossrefGoogle Scholar
  • [22] Peskir G, Shiryaev AN (2006) Optimal Stopping and Free-Boundary Problems, Lectures in Mathematics, ETH Zürich (Birkhäuser, Basel, Switzerland).Google Scholar
  • [23] Shiryaev AN (2010) Quickest detection problems: Fifty years later. Sequential Anal. 29(4):345–385.CrossrefGoogle Scholar
  • [24] Tsitsiklis JN, Van Roy B (1997) Approximate solutions to optimal stopping problems. Advances in Neural Information Processing Systems, vol. 9 (MIT Press, Cambridge, MA).Google Scholar
  • [25] Yin G, Zhu C (2009) Hybrid Switching Diffusions: Properties and Applications, Stochastic Modelling and Applied Probability, vol. 63 (Springer Science & Business Media, New York).Google Scholar
  • [26] Zhang Q, Guo X (2004) Closed-form solutions for perpetual American put options with regime switching. SIAM J. Appl. Math. 64(6):2034–2049.CrossrefGoogle Scholar
  • [27] Zhang Q, Yin G, Liu RH (2005) A near-optimal selling rule for a two-time-scale market model. Multiscale Model. Simul. 4(1):172–193.CrossrefGoogle Scholar
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