Path-Dependent Backward Stochastic Differential Equations with Jumps

2015 ◽  
Author(s):  
Eduard Kromer ◽  
Ludger Overbeck ◽  
Jasmin A.L. RRder
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Backward Stochastic Differential Equations ◽  
Path Dependent

Path-dependent BSDEs with jumps and their connection to PPIDEs

2016 ◽  
Vol 17 (05) ◽  
pp. 1750036 ◽  
Author(s):  
Eduard Kromer ◽  
Ludger Overbeck ◽  
Jasmin A. L. Röder
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Viscosity Solution ◽  
Path Dependence ◽  
Backward Stochastic Differential Equations ◽  
Terminal Condition ◽  
Path Dependent

We study path-dependent backward stochastic differential equations (BSDEs) with jumps. In this context path-dependence of a BSDE is the dependence of the BSDE-terminal condition and the BSDE-generator of a path of a càdlàg process. We study the path-differentiability of BSDEs of this type and establish a connection to path-dependent PIDEs in terms of the existence of a viscosity solution and the respective Feynman–Kac theorem.

DISSIPATIVE BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONS

2006 ◽  
Vol 09 (01) ◽  
pp. 155-168 ◽  
Author(s):  
FULVIA CONFORTOLA
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Infinite Dimensions ◽  
Partial Differential

We prove an existence and uniqueness result for a class of backward stochastic differential equations (BSDE) with dissipative drift in Hilbert spaces. We also give examples of stochastic partial differential equations which can be solved with our result.

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