Game of Singular Stochastic Control and Strategic Exit

Published Online:https://doi.org/10.1287/moor.2014.0700

References

  • Alvarez LHR (1999) A class of solvable singular stochastic control problems. Stochastics Stochastics Rep. 67(1–2):83–122.CrossrefGoogle Scholar
  • Alvarez LHR (2001) Singular stochastic control, linear diffusions, and optimal stopping: A class of solvable problems. SIAM J. Control Optim. 39(6):1697–1710.CrossrefGoogle Scholar
  • Alvarez LHR (2003) On the properties of r-excessive mappings for a class of diffusions. Ann. Appl. Probab. 13(4):1517–1533.CrossrefGoogle Scholar
  • Bather J, Chernoff H (1967) Sequential decisions in the control of a spaceship. Fifth Berkeley Sympos. Math. Statist. Probab., vol. 3 (University of California Press, Berkeley, CA), 181–207.Google Scholar
  • Bayraktar E, Huang YJ (2013) On the multidimensional controller-and-stopper games. SIAM J. Control Optim. 51(2):1263–1297.CrossrefGoogle Scholar
  • Benes V, Shepp L, Witsenhausen H (1980) Some solvable stochastic control problems. Stochastics Stochastics Rep. 4(1):39–83.CrossrefGoogle Scholar
  • Chow P, Menaldi J, Robin M (1985) Additive control of stochastic linear systems with finite horizon. SIAM J. Control Optim. 23(6):858–899.CrossrefGoogle Scholar
  • Davis MHA, Zervos M (1994) A problem of singular stochastic control with discretionary stopping. Ann. Appl. Probab. 4(1):226–240.CrossrefGoogle Scholar
  • Davis MHA, Zervos M (1998) A pair of explicitly solvable singular stochastic control problems. Appl. Math. Optim. 38(3):327–352.CrossrefGoogle Scholar
  • Feichtinger G, Hartl RF, Sethi SP (1994) Dynamic optimal control models in advertising: Recent developments. Management Sci. 40(2):195–226.LinkGoogle Scholar
  • Forde M, Kumar R, Zhang H (2015) Large deviations for the boundary local time of doubly reflected Brownian motion Statist. Probab. Lett., 96:262–268.CrossrefGoogle Scholar
  • Fudenberg D, Tirole J (1991) Game Theory (MIT Press, Cambridge, MA).Google Scholar
  • Grosset L, Viscolani B (2004) Advertising for a new product introduction: A stochastic approach. TOP 12(1):149–167.CrossrefGoogle Scholar
  • Harrison JM (1985) Brownian Motion and Stochastic Flow Systems (John Wiley & Sons, New York).Google Scholar
  • Harrison JM, Taksar MI (1983) Instantaneous control of Brownian motion. Math. Oper. Res. 8(3):439–453.LinkGoogle Scholar
  • Jack A, Johnson TC, Zervos M (2008) A singular control model with application to the goodwill problem. Stochastic Processes Their Appl. 118(11):2098–2124.CrossrefGoogle Scholar
  • Karatzas I (1981) The monotone follower problem in stochastic decison theory. Appl. Math. Optim. 7(1):175–189.CrossrefGoogle Scholar
  • Karatzas I (1983) A class of singular stochastic control problems. Adv. Appl. Probab. 15(2):225–254.CrossrefGoogle Scholar
  • Karatzas I, Shreve SE (1998) Brownian Motion and Stochastic Calculus, 2nd ed. (Springer, New York).CrossrefGoogle Scholar
  • Karatzas I, Sudderth W (2006) Stochastic games of control and stopping for a linear diffusion. Random Walk, Sequential Analysis and Related Topics (World Scientific Publisher, Hackensack, NJ), 100–117.CrossrefGoogle Scholar
  • Karatzas I, Zamfirescu IM (2008) Martingale approach to stochastic differential games of control and stopping. Ann. Probab. 36(4):1495–1527.CrossrefGoogle Scholar
  • Keller JJ (1992) Reaching out: AT&T, MCI, Sprint raise the intensity of their endless war. Wall Street Journal (October 20) A1.Google Scholar
  • Lon PC, Zervos M (2011) A model for optimally advertising and launching a product. Math. Oper. Res. 36(2):363–376.LinkGoogle Scholar
  • Marinelli C (2007) The stochastic goodwill problem. Eur. J. Oper. Res. 176(1):389–404.CrossrefGoogle Scholar
  • Maskin E, Tirole J (2001) Markov perfect equilibrium: I. Observable actions. J. Econom. Theory 100(2):191–219.CrossrefGoogle Scholar
  • Matomäki P (2012) On solvability of a two-sided singular control problem. Math. Methods Oper. Res. 76:239–271.CrossrefGoogle Scholar
  • Myerson RB (2004) Game Theory: Analysis of Conflict (Harvard University Press, Cambridge, MA).Google Scholar
  • Nerlove M, Arrow KJ (1962) Optimal advertising policy under dynamic conditions. Economica 29(114):129–142.CrossrefGoogle Scholar
  • Nilakantan L (1993) Continuous time stochastic games. Unpublished doctoral dissertation, University of Minnesota, Minneapolis.Google Scholar
  • Olver FWJ, Lozier DW, Boisvert RF, Clark CW, eds. (2010) NIST Handbook of Mathematical Functions (Cambridge University Press, Cambridge, UK).Google Scholar
  • Protter PE (2003) Stochastic Integration and Differential Equations (Springer, Berlin).Google Scholar
  • Schelling TC (1980) The Strategy of Conflict (Harvard University Press, Cambridge, MA).Google Scholar
  • Tarski A (1955) A lattice-theoretical fixpoint theorem and its applications. Pacific J. Math. 5(2):285–309.CrossrefGoogle Scholar
  • Zhu H (1992) Generalized solution in singular stochastic control: The nondegenerate problem. Appl. Math. Optim. 25(3):225–245.CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.