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A class of backward stochastic differential equations with discontinuous coefficients. (English) Zbl 1134.60041
Summary: We deal with one-dimensional backward stochastic differential equations (BSDEs) whose coefficient may be discontinuous in $y$ and continuous in $z$. We prove, in this setting, the existence of the solution to BSDEs.

MSC:
60H10Stochastic ordinary differential equations
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References:
[1] El Karoui, N.; Peng, S.; Quenez, M. C.: Backward stochastic differential equations in finance. Math. finance 7, No. 1, 1-71 (1997) · Zbl 0884.90035
[2] Kobylanski, M.: Backward stochastic differential equations and partial differential equations with quadratic growth. Ann. probab. 28, 259-276 (2000) · Zbl 1044.60045
[3] Lepeltier, J. P.; Martin, J. San: Backward stochastic differential equations with continuous coefficients. Statist. probab. Lett. 34, 425-430 (1997) · Zbl 0904.60042
[4] Maugeri, A.; Palagachev, D. K.; Softova, L. G.: Elliptic and parabolic equations with discontinuous coefficients. (2003) · Zbl 0958.35002
[5] Pardoux, E.; Peng, S.: Adapted solution of a backward stochastic differential equation. Systems control lett. 14, 55-61 (1990) · Zbl 0692.93064
[6] Pardoux, E., Peng, S., 1992. Backward stochastic differential equations and quasilinear parabolic partial differential equations. In: Rozovskii, B., Sowers, R. (Eds.), Stochastic Differential Equations and their Applications. Lecture Notes in Control and Information Sciences, vol. 176. Springer, Berlin, pp. 200 -- 217. · Zbl 0766.60079
[7] Peng, S.: Probabilistic interpretation for systems of quasilinear parabolic partial differential equations. Stochastics stochastic reports 37, 61-74 (1991) · Zbl 0739.60060
[8] Peng, S.: A generalized dynamic programming principle and Hamilton -- Jacobi -- Bellman equation. Stochastics stochastic reports 38, 119-134 (1992) · Zbl 0756.49015
[9] Peng, S., 2004. Nonlinear expectations, nonlinear evaluations and risk measures. In: Frittelli, M., Runggaldier, W. (Eds.), Stochastic Methods in Finance. Lecture Notes in Mathematics, vol. 1856. Springer, Berlin, pp. 165 -- 253. · Zbl 1127.91032