메뉴 건너뛰기




Volumn 16, Issue 3, 2009, Pages 381-420

Probabilistic interpretation for systems of Isaacs equations with two reflecting barriers

Author keywords

Dynamic programming principle; Isaacs equations with obstacles; Reflected backward stochastic differential equations; Stochastic differential games; Value function; Viscosity solution; Zero sum games

Indexed keywords


EID: 70349811505     PISSN: 10219722     EISSN: 14209004     Source Type: Journal    
DOI: 10.1007/s00030-009-0022-0     Document Type: Article
Times cited : (21)

References (27)
  • 1
    • 0002508109 scopus 로고    scopus 로고
    • Backward stochastic differential equations and integral-partial differential equations
    • Barles G., Buckdahn R., Pardoux E.: Backward stochastic differential equations and integral-partial differential equations. Stoch. Stoch. Rep. 60, 57-83 (1997).
    • (1997) Stoch. Stoch. Rep. , vol.60 , pp. 57-83
    • Barles, G.1    Buckdahn, R.2    Pardoux, E.3
  • 2
    • 16244414648 scopus 로고    scopus 로고
    • Nash equilibrium payoffs for nonzero-sum stochastic differential games
    • Buckdahn R., Cardaliaguet P., Rainer C.: Nash equilibrium payoffs for nonzero-sum stochastic differential games. SIAM J. Cont. Opt. 43(2), 624-642 (2004).
    • (2004) SIAM J. Cont. Opt. , vol.43 , Issue.2 , pp. 624-642
    • Buckdahn, R.1    Cardaliaguet, P.2    Rainer, C.3
  • 3
    • 55349131010 scopus 로고    scopus 로고
    • Stochastic differential games and viscosity solutions of Hamilton-Jacobi-Bellman-Isaacs equations
    • doi:10.1137/060671954
    • Buckdahn R., LI J.: Stochastic differential games and viscosity solutions of Hamilton-Jacobi-Bellman-Isaacs equations. SIAM J. Cont. Opt. 47(1), 444-475 (2008). doi:10.1137/060671954.
    • (2008) SIAM J. Cont. Opt. , vol.47 , Issue.1 , pp. 444-475
    • Buckdahn, R.1    Li, J.2
  • 4
    • 70349818900 scopus 로고    scopus 로고
    • Buckdahn, R., LI, J.: Stochastic differential games with reflection and related obstacle problems for Isaacs equations. Submitted. (2007) Available online
    • Buckdahn, R., LI, J.: Stochastic differential games with reflection and related obstacle problems for Isaacs equations. Submitted. (2007) Available online: http://arxiv.org/abs/0707.1133.
  • 5
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • Crandall M.G., Ishii H., Lions P.L.: User's guide to viscosity solutions of second order partial differential equations. Bull. Am. Math. Soc. 27, 1-67 (1992).
    • (1992) Bull. Am. Math. Soc. , vol.27 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.L.3
  • 6
    • 0030360242 scopus 로고    scopus 로고
    • Backward SDE's with reflection and Dynkin Games
    • Cvitanic J., Karatzas I.: Backward SDE's with reflection and Dynkin Games. Ann. Probab. 24, 2024-2056 (1996).
    • (1996) Ann. Probab. , vol.24 , pp. 2024-2056
    • Cvitanic, J.1    Karatzas, I.2
  • 7
    • 70349812816 scopus 로고    scopus 로고
    • Dellacherie, C.: Sur l'existence de certains essinf et esssup de familles de processus mesuables. In: Sem. Probab. XII. Lecture Notes in Math. vol. 649, pp. 512-514. Springer-Verlag, Berlin (1977)
    • Dellacherie, C.: Sur l'existence de certains essinf et esssup de familles de processus mesuables. In: Sem. Probab. XII. Lecture Notes in Math. vol. 649, pp. 512-514. Springer-Verlag, Berlin (1977).
  • 9
    • 0031542653 scopus 로고    scopus 로고
    • Backward stochastic differential equations in finance
    • El Karoui N., Peng S., Quenez M.C.: Backward stochastic differential equations in finance. Math. Finance. 7(1), 1-71 (1997).
    • (1997) Math. Finance. , vol.7 , Issue.1 , pp. 1-71
    • El Karoui, N.1    Peng, S.2    Quenez, M.C.3
  • 10
    • 0031483012 scopus 로고    scopus 로고
    • Reflected solutions of backward SDE's, and related obstacle problems for PDE's
    • El Karoui N., Kapoudjian C., Pardoux E., Peng S., Quenez M.C.: Reflected solutions of backward SDE's, and related obstacle problems for PDE's. Ann. Probab 25(2), 702-737 (1997).
    • (1997) Ann. Probab , vol.25 , Issue.2 , pp. 702-737
    • El Karoui, N.1    Kapoudjian, C.2    Pardoux, E.3    Peng, S.4    Quenez, M.C.5
  • 11
    • 70349825009 scopus 로고    scopus 로고
    • El Karoui, N., Pardoux, E., Quenez, M.C.: Reflected backward SDEs and American options. In: Numerical methods in finance. Publ. Newton Inst. pp. 215-231. Cambridge University Press, Cambridge (1997)
    • El Karoui, N., Pardoux, E., Quenez, M.C.: Reflected backward SDEs and American options. In: Numerical methods in finance. Publ. Newton Inst. pp. 215-231. Cambridge University Press, Cambridge (1997).
  • 12
    • 0000097584 scopus 로고
    • On the existence of value functions of two-player, zero-sum stochastic differential games
    • Fleming W.H., Souganidis P.E.: On the existence of value functions of two-player, zero-sum stochastic differential games. Indiana Univ. Math. J. 38(2), 293-314 (1989).
    • (1989) Indiana Univ. Math. J. , vol.38 , Issue.2 , pp. 293-314
    • Fleming, W.H.1    Souganidis, P.E.2
  • 13
    • 33947240908 scopus 로고    scopus 로고
    • Mixed zero-sum stochastic differential game and American game option
    • Hamadène S.: Mixed zero-sum stochastic differential game and American game option. SIAM J. Con. Opt. 45, 496-518 (2006).
    • (2006) SIAM J. Con. Opt. , vol.45 , pp. 496-518
    • Hamadène, S.1
  • 14
    • 0029276198 scopus 로고
    • Zero-sum stochastic differential games and backward equations
    • Hamadène S., Lepeltier J.P.: Zero-sum stochastic differential games and backward equations. Syst. Control Lett. 24, 259-263 (1995).
    • (1995) Syst. Control Lett. , vol.24 , pp. 259-263
    • Hamadène, S.1    Lepeltier, J.P.2
  • 16
    • 1642360307 scopus 로고    scopus 로고
    • Double barrier reflected backward stochastic differential equations with continuous coefficient
    • Hamadène S., Lepeltier J.P., Matoussi A.: Double barrier reflected backward stochastic differential equations with continuous coefficient. Pitman Res. Notes. Math. Ser. 364, 115-128 (1997).
    • (1997) Pitman Res. Notes. Math. Ser. , vol.364 , pp. 115-128
    • Hamadène, S.1    Lepeltier, J.P.2    Matoussi, A.3
  • 17
    • 70349830960 scopus 로고    scopus 로고
    • Hamadène, S., Lepeltier, J.P., Peng, S.: BSDEs with continuous coefficients and stochastic differential games. In: El Karoui, N., Mazliak, L. (eds.) Backward Stochastic Differential Equations. Pitman Res. Notes Math. Ser., vol. 364, pp. 115-128. Longman, Harlow (1997)
    • Hamadène, S., Lepeltier, J.P., Peng, S.: BSDEs with continuous coefficients and stochastic differential games. In: El Karoui, N., Mazliak, L. (eds.) Backward Stochastic Differential Equations. Pitman Res. Notes Math. Ser., vol. 364, pp. 115-128. Longman, Harlow (1997).
  • 18
    • 33644553811 scopus 로고    scopus 로고
    • BSDEs with two reflecting barriers: The general result
    • Hamadène S., Hassani M.: BSDEs with two reflecting barriers: the general result. Probab. Theory Relat. Fields 132, 237-264 (2005).
    • (2005) Probab. Theory Relat. Fields , vol.132 , pp. 237-264
    • Hamadène, S.1    Hassani, M.2
  • 19
    • 44649173136 scopus 로고    scopus 로고
    • Switching games of stochastic differential systems
    • Hou S., Tang S.: Switching games of stochastic differential systems. SIAM J. Cont. Opt. 46(3), 900-929 (2007).
    • (2007) SIAM J. Cont. Opt. , vol.46 , Issue.3 , pp. 900-929
    • Hou, S.1    Tang, S.2
  • 23
    • 14844352406 scopus 로고    scopus 로고
    • Reflected forward-backward SDEs and obstacle problems with boundary conditions
    • Ma J., Cvitanic J.: Reflected forward-backward SDEs and obstacle problems with boundary conditions. J. Appl. Math. Stoch. Anal. 14(2), 113-138 (2001).
    • (2001) J. Appl. Math. Stoch. Anal. , vol.14 , Issue.2 , pp. 113-138
    • Ma, J.1    Cvitanic, J.2
  • 24
    • 0025262967 scopus 로고
    • Adapted solution of a backward stochastic differential equation
    • Pardoux E., Peng S.: Adapted solution of a backward stochastic differential equation. Syst. Control Lett. 14(1-2), 61-74 (1990).
    • (1990) Syst. Control Lett. , vol.14 , Issue.1-2 , pp. 61-74
    • Pardoux, E.1    Peng, S.2
  • 25
    • 70349790995 scopus 로고    scopus 로고
    • Peng, S.: BSDE and stochastic optimizations. In: Yan, J., Peng, S., Fang, S., Wu, L. (eds.) Topics in Stochastic Analysis, Ch.2. Science Press. Beijing (in Chinese) (1997)
    • Peng, S.: BSDE and stochastic optimizations. In: Yan, J., Peng, S., Fang, S., Wu, L. (eds.) Topics in Stochastic Analysis, Ch.2. Science Press. Beijing (in Chinese) (1997).
  • 26
    • 0001098095 scopus 로고
    • A generalized dynamic programming principle and Hamilton-Jacobi-Bellman equation
    • Peng S.: A generalized dynamic programming principle and Hamilton-Jacobi-Bellman equation. Stoch. Stoch. Reports. 38, 119-134 (1992).
    • (1992) Stoch. Stoch. Reports. , vol.38 , pp. 119-134
    • Peng, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.