Backward stochastic differential equations with Markov switching driven by Brownian motion and Poisson random measure

References

• G.Barles, R.Buckdahn, and E.Pardoux, Backward stochastic differential equations and integral–partial differential equations, Stoch. Stoch. Rep.60(1–2) (1997), pp. 57–83.
   Google Scholar
• D.Becherer, Bounded solutions to backward SDE's with jumps for utility optimization and indifference hedging, Ann. Appl. Probab.16(4) (2006), pp. 2027–2054.
   Web of Science ®Google Scholar
• J.M.Bismut, Conjugate convex functions in optimal stochastic control, J. Math. Anal. Appl.44(2) (1973), pp. 384–404.
   Web of Science ®Google Scholar
• J.M.Bismut, Controle des systemes Lineaires Quadratiques: Applications de l'integrals Stochastique, Lecture Notes Math. Vol. 649Springer-Verlag, Berlin, 1978.
   Google Scholar
• R.Boel and P.Varaiya, Optimal control of jump processes, SIAM J. Control Optim.15(1) (1977), pp. 92–119.
   Web of Science ®Google Scholar
• S.Cohen and R.Elliott, Solutions of backward stochastic differential equations on Markov chains, Commun. Stoch. Anal.2(2) (2008), pp. 251–262.
   Google Scholar
• S.Cohen and R.Elliott, Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions, Ann. Appl. Probab.20(1) (2010), pp. 267–311.
   Web of Science ®Google Scholar
• N.El Karoui, S.G.Peng, and M.C.Quenez, Backward stochastic differential equations in finance, Math. Finance7(1) (1997), pp. 1–71.
   Web of Science ®Google Scholar
• N.Ikeda and S.Watanabe, Stochastic Differential Equations and Diffusion Processes, 2nd ed., North-Holland Mathematical Library, Amsterdam, 1989.
   Google Scholar
• Y.D.Ji and H.J.Chizeck, Jump linear quadratic Gaussian control in continuous-time, IEEE Trans. Autom. Control37(12) (1992), pp. 1884–1892.
   Web of Science ®Google Scholar
• Z.Jin, G.Yin, and F.K.Wu, Optimal reinsurance strategies in regime-switching jump diffusion models: Stochastic differential game formulation and numerical methods, Insurance Math. Econ.53(3) (2013), pp. 733–746.
   Web of Science ®Google Scholar
• X.Li and X.Y.Zhou, Indefinite stochastic LQ controls with Markovian jumps in a finite time horizon, Commun. Inf. Syst.2(3) (2002), pp. 265–282.
   Google Scholar
• J.W.Luo, Comparison principle and stability of Itô stochastic differential delay equations with Poisson jump and Markovian switching, Nonlinear Anal.64(1) (2006), pp. 253–262.
   Web of Science ®Google Scholar
• J.Ma and J.M.Yong, Forward-Backward Stochastic Differential Equations and Their Applications, Lecture Notes Math. Vol. 1702Springer-Verlag, Berlin, 1999.
   Google Scholar
• M.A.Morlais, Utility maximization in a jump market model, Stochastics81(1) (2009), pp. 1–27.
   Google Scholar
• M.A.Morlais, A new existence result for quadratic BSDEs with jumps with application to the utility maximization problem, Stoch. Proc. Appl.120(10) (2010), pp. 1966–1995.
   Web of Science ®Google Scholar
• E.Pardoux and S.G.Peng, Adapted solution of a backward stochastic differential equation, Syst. Control Lett.14(1) (1990), pp. 55–61.
   Web of Science ®Google Scholar
• E.Pardoux and S.G.Peng, Backward doubly stochastic differential equations and systems of quasilinear SPDEs, Probab. Theory Relat. Fields98(2) (1994), pp. 209–227.
   Web of Science ®Google Scholar
• E.Pardoux and S.J.Tang, Forward-backward stochastic differential equations and quasilinear parabolic PDEs, Probab. Theory Relat. Fields114(2) (1999), pp. 123–150.
   Web of Science ®Google Scholar
• S.G.Peng, Probabilistic interpretation for systems of quasilinear parabolic partial differential equations, Stoch. Stoch. Rep.37(1–2) (1991), pp. 61–74.
   Google Scholar
• S.G.Peng, Backward stochastic differential equations and applications to optimal control, Appl. Math. Optim.27(2) (1993), pp. 125–144.
   Web of Science ®Google Scholar
• R.Rishel, A mimimum principle for controlled jump processes, in Control Theory, Numerical Methods and Computer Systems Modelling, A.Bensoussan and J.L.Lions, eds., Lecture Notes Econ. Math. Sys. Vol. 107, Springer-Verlag, Berlin, 1975, pp. 493–508.
   Google Scholar
• M.Royer, Backward stochastic differential equations with jumps and related non-linear expectations, Stoch. Proc. Appl.116(10) (2006), pp. 1358–1376.
   Web of Science ®Google Scholar
• R.Situ, On solutions of backward stochastic differential equations with jumps and applications, Stoch. Proc. Appl.66(2) (1997), pp. 209–236.
   Web of Science ®Google Scholar
• Q.S.Song, G.Yin, and Z.M.Zhang, Numerical method for controlled regime-switching diffusions and regime-switching jump diffusions, Automatica42(7) (2006), pp. 1147–1157.
   Web of Science ®Google Scholar
• S.J.Tang and X.J.Li, Necessary conditions for optimal control of stochastic systems with random jumps, SIAM J. Control Optim.32(5) (1994), pp. 1447–1475.
   Web of Science ®Google Scholar
• H.B.Tang and Z.Wu, Backward stochastic differential equations with Markov chains and related asymptotic properties, Adv. Differ. Equ.285 (2013), p. 17.
   Google Scholar
• Z.Wu and X.R.Wang, FBSDE with Poisson processes and its application to linear quadratic stochastic optimal control problem with random jumps, Acta Autom. Sin.29(6) (2003), pp. 821–826.
   Google Scholar
• S.J.Yan and X.F.Liu, Measure and Probability, Chinese version, 2nd ed., Beijing Normal University Press, Beijing, 2003.
   Google Scholar
• J.L.Yin and X.R.Mao, The adapted solution and comparison theorem for backward stochastic differential equations with Poisson jumps and applications, J. Math. Anal. Appl.346(2) (2008), pp. 345–358.
   Web of Science ®Google Scholar
• J.M.Yong and X.Y.Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer-Verlag, New York, 1999.
   Google Scholar
• X.Y.Zhou and G.Yin, Markowitz's mean-variance portfolio selection with regime switching: A continuous-time model, SIAM J. Control Optim.42(4) (2003), pp. 1466–1482.
   Web of Science ®Google Scholar