A new kind of backward stochastic differential equations (in short BSDE), where the solution is a pair of processes adapted to the past of the driving Brownian motion, has been introduced by theâ€¦ (More)

We introduce a notion of nonlinear expectation â€”-Gâ€“expectationâ€”generated by a nonlinear heat equation with a given infinitesimal generator G. We first discuss the notion of Gâ€“standard normalâ€¦ (More)

From a general deenition of nonlinear expectations, viewed as operators preserving monotonicity and constants, we derive, under rather general assumptions, the notions of conditional nonlinearâ€¦ (More)

We develop a notion of nonlinear expectation â€”-Gâ€“expectationâ€”generated by a nonlinear heat equation with infinitesimal generator G. We first study multi-dimensional Gâ€“normal distributions. With thisâ€¦ (More)

In this paper, we discuss a new type of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes notâ€¦ (More)

In [5] the authors obtained Mean-Field backward stochastic differential equations (BSDE) associated with a Mean-field stochastic differential equation (SDE) in a natural way as limit of some highlyâ€¦ (More)

Existence and uniqueness results of fully coupled forward-backward stochastic differential equations with an arbitrarily large time duration are obtained. Some stochastic Hamilton systems arising inâ€¦ (More)

In [1], Z. Chen proved that, if for each terminal condition Î¾, the solution of the BSDE associated to the standard parameter (Î¾, g1) is equal at time t = 0 to the solution of the BSDE associated toâ€¦ (More)

How an agent (or a firm, an investor, a financial market) evaluates a contingent claim, say a European type of derivatives X, with maturity t? In this paper we study a dynamic evaluation of thisâ€¦ (More)