ADJOINT FORWARD BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY JUMP DIFFUSION PROCESSES AND ITS APPLICATION TO NONLINEAR FILTERING PROBLEMS

2019 ◽  
Vol 9 (2) ◽  
pp. 143-159
Author(s):  
Feng Bao ◽  
Yanzhao Cao ◽  
Hongmei Chi
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Nonlinear Filtering ◽  
Diffusion Processes ◽  
Jump Diffusion ◽  
Backward Stochastic Differential Equations ◽  
Jump Diffusion Processes

AN ERGODIC BSDE RISK REPRESENTATION IN A JUMP-DIFFUSION FRAMEWORK

2021 ◽  
pp. 2150015
Author(s):  
CALISTO GUAMBE ◽  
LESEDI MABITSELA ◽  
RODWELL KUFAKUNESU
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Risk Measures ◽  
Risk Measure ◽  
Jump Diffusion ◽  
Backward Stochastic Differential Equations ◽  
Financial Position ◽  
Entropic Risk Measure ◽  
Risk Representation

We consider the representation of forward entropic risk measures using the theory of ergodic backward stochastic differential equations in a jump-diffusion framework. Our paper can be viewed as an extension of the work considered by Chong et al. (2019) in the diffusion case. We also study the behavior of a forward entropic risk measure under jumps when a financial position is held for a longer maturity.

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