Backward Stochastic Differential Equations and Risk Measures

2019 ◽  
pp. 75-91
Author(s):  
Bernt Øksendal ◽  
Agnès Sulem
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Risk Measures ◽  
Backward Stochastic Differential Equations

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.

scholarly journals Dynamic Risk Measures for Processes via Backward Stochastic Differential Equations Associated with Lévy Processes

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 741
Author(s):  
Liangliang Miao ◽  
Zhang Liu ◽  
Yijun Hu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Lévy Processes ◽  
Risk Measures ◽  
Time Consistency ◽  
Levy Processes ◽  
Backward Stochastic Differential Equations ◽  
Dynamic Risk Measures ◽  
Numerical Examples ◽  
Dynamic Risk

In this paper, we study the dynamic risk measures for processes induced by backward stochastic differential equations driven by Teugel’s martingales associated with Lévy processes (BSDELs). The representation theorem for generators of BSDELs is provided. Furthermore, the time consistency of the coherent and convex dynamic risk measures for processes is characterized by means of the generators of BSDELs. Moreover, the coherency and convexity of dynamic risk measures for processes are characterized by the generators of BSDELs. Finally, we provide two numerical examples to illustrate the proposed dynamic risk measures.

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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