Nonzero-sum risk-sensitive stochastic differential games with discounted costs

References

• Borkar, V. S., 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. DOI: 10.1007/BF02192034.
   Web of Science ®Google Scholar
• Elliott, R. J., Davis, M. H. A. (1981). Optimal play in a stochastic differential game. SIAM J. Control Optim. 19(4):543–554. DOI: 10.1137/0319033.
   Web of Science ®Google Scholar
• Varaiya, P. (1976). N-player stochastic differential games. SIAM J. Control Optim. 14(3):538–545. DOI: 10.1137/0314036.
   Google Scholar
• Basar, T. (1999). Nash equilibria of risk-sensitive nonlinear stochastic differential games. J. Optim. Theory Appl. 100:479–498.
   Web of Science ®Google Scholar
• Basu, A., Ghosh, M. K. (2012). Risk-sensitive stochastic differential games. Math OR. 37(3):437–449. DOI: 10.1287/moor.1120.0542.
   Google Scholar
• Biswas, A., Saha, S. (2020). Zero-sum stochastic differential games with risk-sensitive cost. Appl. Math. Optim. 81(1):113–140. DOI: 10.1007/s00245-018-9479-8.
   Web of Science ®Google Scholar
• El Karoui, N., Hamadene, S. (2003). BSDE and risk-sensitive control, zero-sum and nonzero-sum game problems of stochastic functional differential equations. Stoch. Process. Appl. 107:145–169.
   Web of Science ®Google Scholar
• Bell, D. E. (1995). Risk, return and utility. Manage. Sci. 41(1):23–30. DOI: 10.1287/mnsc.41.1.23.
   Web of Science ®Google Scholar
• Nowak, A. S. (2005). Notes on risk-sensitive Nash equilibria. In: Andrzej S. Nowak, Krzysztof Szajowski, eds. Advances in Dynamic Games. Annals of the International Society of Dynamic Games. Vol. 7. Boston, MA: Birkhauser Boston, pp. 95–109.
   Google Scholar
• Bellman, R. (1957). Dynamic Programming. Princeton, NJ: Princeton University Press.
   Google Scholar
• Whittle, P. (1990). Risk-Sensitive Optimal Control. Wiley-Interscience Series in Systems and Optimization. Chichester: John Wiley & Sons, Ltd.
   Google Scholar
• Arapostathis, A., Biswas, A. (2018). Infinite horizon risk-sensitive control of diffusions without any blanket stability assumptions. Stoch. Process. Appl. 128(5):1485–1524. DOI: 10.1016/j.spa.2017.08.001.
   Web of Science ®Google Scholar
• Bensoussan, A., Nagai, H. (1997). Min-max characterization of a small noise limit on risk-sensitive control. SIAM J. Control Optim. 35(4):1093–1115. DOI: 10.1137/S0363012995279420.
   Web of Science ®Google Scholar
• Bensoussan, A., Frehse, J., Nagai, H. (1998). Some results on risk-sensitive control with full observation. Appl. Math. Optim. 37(1):1–41. DOI: 10.1007/s002459900067.
   Web of Science ®Google Scholar
• Biswas, A. (2011). Risk sensitive control of diffusions with small running cost. Appl. Math. Optim. 64(1):1–12. DOI: 10.1007/s00245-010-9127-4.
   Web of Science ®Google Scholar
• Biswas, A., Borkar, V. S., Kumar, K. S. (2010). 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. DOI: 10.1007/s00245-010-9119-4.
   Web of Science ®Google Scholar
• Fleming, W. H., Hernández-Hernández, D. (2011). On the value of stochastic differential games. Comm. Stoch. Anal. 5:341–351.
   Google Scholar
• Fleming, W. H., McEneaney, W. M. (1995). Risk-sensitive control on an infinite time horizon. SIAM J. Control Optim. 33(6):1881–1915. DOI: 10.1137/S0363012993258720.
   Web of Science ®Google Scholar
• Jacobson, D. H. (1973). Optimal stochastic linear systems with exponential performance criteria and their relation to deterministic differential games. IEEE Trans. Autom. Control. 18(2):124–131. DOI: 10.1109/TAC.1973.1100265.
   Web of Science ®Google Scholar
• Menaldi, J.-L., Robin, M. (2005). Remarks on risk-sensitive control problems. Appl. Math. Optim. 52(3):297–310. DOI: 10.1007/s00245-005-0829-y.
   Web of Science ®Google Scholar
• Nagai, H. (2003). Optimal strategies for risk-sensitive portfolio optimization problems for general factor models. SIAM J. Control Optim. 41(6):1779–1800. DOI: 10.1137/S0363012901399337.
   Web of Science ®Google Scholar
• Runolfsson, T. (2000). Robust control of discrete-time hybrid systems with uncertain modal dynamics. Math. Prob. Eng. 5(6):459–478. DOI: 10.1155/S1024123X99001192.
   Google Scholar
• Arapostathis, A., Borkar, V. S., Ghosh, M. K. (2012). Ergodic Control of Diffusion Processes, Encyclopedia of Mathematics and Its Applications 143. Cambridge University Press.
   Google Scholar
• Warga, J. (1967). Functions of relaxed controls. SIAM J. Control. 5(4):628–641. DOI: 10.1137/0305042.
   Google Scholar
• Bensoussan, A., Lions, J. L. (1984). Impulse Control and Quasi-Variational Inequalities. Bristol: Gauthier-Villars.
   Google Scholar
• Ladyzhenskaya, O. A., Solonnikov, V. A., Uraltseva, N. N. (1968). Linear and Quasilinear Equations of Parabolic Type. Providence, RI: American Mathematical Society.
   Google Scholar
• Beneš, V. E. (1970). Existence of optimal strategies based on specified information, for a class of stochastic decision problems. SIAM J. Control. 8:179–188.
   Web of Science ®Google Scholar
• Okada, N. (1984). On the Banach-Saks Property. Proc. Japan Acad. Ser. A Math. Sci. 60(7):246–248. DOI: 10.3792/pjaa.60.246.
   Google Scholar
• Fan, K. (1952). Fixed-point and minimax theorems in locally convex topological linear spaces. Proc. Natl. Acad. Sci. USA 38(2):121–126. DOI: 10.1073/pnas.38.2.121.
   PubMed Web of Science ®Google Scholar