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Backward stochastic differential equations in finance. (English) Zbl 0884.90035
We are concerned with backward stochastic differential equations (BSDE) and with their applications to finance. These equations were introduced by Bismut (1973) for the linear case and by Pardoux and Peng (1990) in the general case. According to these authors, the solution of a BSDE consists of a pair of adapted processes \((Y,Z)\) satisfying \[ -dY_t= f(t,Y_t,Z_t)dt- Z_t^* dW_t; \qquad Y_T=\xi, \] where \(f\) is the generator and \(\xi\) is the terminal condition. Actually, this type of equation appears in numerous problems in finance (as pointed out in Quenez’s doctorate 1993).

91G80 Financial applications of other theories
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
91B62 Economic growth models
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