Backward stochastic differential equations in finance.

*(English)*Zbl 0884.90035We 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

$$-d{Y}_{t}=f(t,{Y}_{t},{Z}_{t})dt-{Z}_{t}^{*}d{W}_{t};\phantom{\rule{2.em}{0ex}}{Y}_{T}=\xi ,$$

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 Quenezâ€™s doctorate 1993).

##### MSC:

91B28 | Finance etc. (MSC2000) |

60H10 | Stochastic ordinary differential equations |

91B62 | Growth models in economics |