Infinite time interval BSDEs and the convergence of g-martingales

Abstract In this paper, we first give a sufficient condition on the coefficients of a class of infinite time interval backward stochastic differential equations (BSDEs) under which the infinite time interval BSDEs have a unique solution for any given square integrable terminal value, and then, using the infinite time interval BSDEs, we study the convergence of g-martingales introduced by Peng via a kind of BSDEs. Finally, we study the applications of g-expectations and g-martingales in both finance and economics.

[1]  J. Lepeltier,et al.  Zero-sum stochastic differential games and backward equations , 1995 .

[2]  N. Karoui,et al.  Dynamic Programming and Pricing of Contingent Claims in an Incomplete Market , 1995 .

[3]  CONTINUOUS PROPERTIES OF G-MARTINGALES , 2001 .

[4]  I. Gilboa,et al.  Maxmin Expected Utility with Non-Unique Prior , 1989 .

[5]  J. Lepeltier,et al.  Backward stochastic differential equations with continuous coefficient , 1997 .

[6]  R. Darling,et al.  BACKWARDS SDE WITH RANDOM TERMINAL TIME AND APPLICATIONS TO SEMILINEAR ELLIPTIC PDE , 1997 .

[7]  Said Hamadène,et al.  Backward equations, stochastic control and zero-sum stochastic differential games , 1995 .

[8]  Shige Peng,et al.  A general downcrossing inequality for g-martingales , 2000 .

[9]  Shige Peng,et al.  Probabilistic interpretation for systems of quasilinear parabolic partial differential equations , 1991 .

[10]  S. Peng,et al.  Solution of forward-backward stochastic differential equations , 1995 .

[11]  Larry G. Epstein,et al.  Intertemporal Asset Pricing Under Knightian Uncertainty , 1994 .

[12]  Jakša Cvitanić,et al.  HEDGING OPTIONS FOR A LARGE INVESTOR AND FORWARD-BACKWARD SDE'S , 1996 .

[13]  L. Wasserman,et al.  Bayes' Theorem for Choquet Capacities , 1990 .

[14]  Larry G. Epstein.  A definition of uncertainty aversion , 1999 .

[15]  S. Peng,et al.  Backward Stochastic Differential Equations in Finance , 1997 .

[16]  Larry G. Epstein,et al.  Uncertainty, Risk-Neutral Measures and Security Price Booms and Crashes , 1995 .

[17]  D. Schmeidler.  Subjective Probability and Expected Utility without Additivity , 1989 .

[18]  S. Peng.  A general stochastic maximum principle for optimal control problems , 1990 .

[19]  S. Peng.  Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob–Meyers type , 1999 .

[20]  R. Darling.  Constructing Gamma-Martingales with Prescribed Limit, Using Backwards SDE , 1995 .

[21]  D. Kramkov.  Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets , 1996 .

[22]  Larry G. Epstein,et al.  Stochastic differential utility , 1992 .

[23]  É. Pardoux,et al.  Generalized BSDEs and nonlinear Neumann boundary value problems , 1998 .

[24]  S. Peng,et al.  Adapted solution of a backward stochastic differential equation , 1990 .

[25]  Jakša Cvitanić,et al.  Hedging Contingent Claims with Constrained Portfolios , 1993 .