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Uniqueness of adapted solutions to scalar BSDEs with Peano-type generators
Shengjun Fan, Ying Hu, Shanjian Tang
A Backward Stochastic Differential Equation (BSDE) with a Peano-type generator, is known to have infinitely many solutions when the terminal value is vanishing, and is shown to hav…
Multi-dimensional non-Markovian backward stochastic differential equations of interactively quadratic generators
Shengjun Fan, Ying Hu, Shanjian Tang
This paper is devoted to a general solvability of multi-dimensional non-Markovian backward stochastic differential equations (BSDEs) with interactively quadratic generators. Some g…
Unbounded Dynamic Concave Utilities via BSDEs
Shengjun Fan, Ying Hu, Shanjian Tang
The dynamic concave utility (or the dynamic convex risk measure) of an unbounded endowment is studied and represented as the value process in the unique solution of a backward stoc…
1D nonlinear backward stochastic differential equations: a unified theory and applications
Shengjun Fan, Ying Hu, Shanjian Tang
Since the celebrated paper by El Karoui, Peng and Quenez [Mathematical Finance, 7 (1997), 1--71], backward stochastic differential equations have found wide applications in stochas…