Pré-Publication, Document De Travail Année : 2025

Uniqueness of adapted solutions to scalar BSDEs with Peano-type generators

Ying Hu
  • Fonction : Auteur
  • PersonId : 829971
  • IdHAL : ying-hu
Shanjian Tang
  • Fonction : Auteur
  • PersonId : 968042

Résumé

It is well known that a Backward Stochastic Differential Equation (BSDE) with a Peano-type generator has infinite many solutions when the terminal value is zero. In this paper, we study the uniqueness of adapted solutions of such a BSDE when the terminal value is positive. Two methods are developed. The first one is to connect the BSDE to an optimal stochastic control problem: under suitable integrability of the terminal value, with a verification argument, we prove that the first component of the adapted solution pair is the value process for some given stochastic optimal control problem. The second one appeals to a change of variables, with a flavor of more analyses: by a change of variables, the original BSDE is reduced to a convex quadratic BSDE, and then using the θ-difference method, we give a sharp result in some special case which can be applied to the BSDE defined by Kreps-Porteus utility.

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hal-05327414 , version 1 (23-10-2025)

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Shengjun Fan, Ying Hu, Shanjian Tang. Uniqueness of adapted solutions to scalar BSDEs with Peano-type generators. 2025. ⟨hal-05327414⟩
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