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Original Articles

Risk-sensitive stochastic differential games with reflecting diffusions

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Pages 1-27 | Received 21 Jun 2017, Accepted 14 Jul 2017, Published online: 26 Sep 2017

References

  • Adams, R. A. 1975. Sobolev Spaces. New York: Academic Press.
  • Arapostathis, A., Borkar, V. S., and Ghosh, M. K. 2012. Ergodic Control of Diffusion Processes. Cambridge University Press, Cambridge, U.K.
  • Basu, A., and Ghosh, M. K. 2012. Zero-sum risk-sensitive stochastic differential games. Math. Oper. Res. 37(3):437–449.
  • Benes̆, V. E. 1970. Existence of optimal strategies based on specified information of a class of stochastic decision problems. SIAM J. Control. 8(2):179–188.
  • Bensoussan, A., and Lions, J. L. 1984. Impulse Control and Quasi-variational Inequalities. England: Gauthier-Villars.
  • Biswas, A., Borkar, V. S., and Kumar, S. K. 2009. Risk-sensitive control with near monotone cost. Appl. Math. Optim. 62(2):145–163. Errata corriege I. 2010. ibid 62(2):165–167. Errata corriege II. 2010. ibid 62(3):435–438.
  • Borkar, V. S. 1989. Optimal control of diffusion processes. In Pitman Research Notes in Mathematics Series. 203. Longman, Harlow U.K..
  • Borkar, V. S., and Ghosh, M. K. 1992. Stochastic differential games: Occupation measure based approach. J. Optim. Theory Appl. 73(2):359–385. Errata corriege. 1996. ibid 88:251–252.
  • Fan, K. 1952. Fixed-point and minimax theorems in locally convex topological linear spaces. Proc. Nat. Acad. Sc. 38(2):121–126.
  • Ghosh, M. K., and Kumar, S. K. 1997. Zero-sum stochastic differential games with reflecting diffusions. Comput. Appl. Math. 16(3):237–246.
  • Ghosh, M. K., and Kumar, S. K. 1999. Nonzero-sum risk-sensitive stochastic differential games with reflecting diffusions. Comput. Appl. Math. 18(3):355–368.
  • Ghosh, M. K., Kumar, S. K., and Pal, C. Nonzero-sum risk-sensitive stochastic differential games. arXiv:1604.01142.
  • Lions, P. L., and Sznitman, A. S. 1984. Stochastic differential equations with reflecting boundary conditions. Comm. Pure. Appl. Math. 37(4):511–537.
  • Menaldi, J. L., and Robin, M. 1984. An ergodic control problem for reflected diffusion with jump. IMA Journal of Mathematical Control & Information 1(4):309–322.
  • Menaldi, J. L., and Robin, M. 2005. Remarks on risk-sensitive control problems. Appl. Math. Optim. 52(3):297–310.
  • Nowak, A. S. 2005. Notes on risk-sensitive Nash equilibria. Advances in dynamic games, Ann. International. Soc. Dynam. Games, 7:95–109.
  • Warga, J. 1967. Functions of relaxed controls. SIAM J. Control. 5(4):628–641.

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