A unified approach to well-posedness of type-I backward stochastic Volterra integral equations
| Autor: | Camilo Hernández, Dylan Possamaï |
|---|---|
| Přispěvatelé: | Columbia University [New York], Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich] (ETH Zürich) |
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Current (mathematics) Statistics & Probability Type (model theory) Backward stochastic Volterra integral equations consistent planning equilibrium Hamilton–Jacobi–Bellman equation representation of partial differential equations Time inconsistency 01 natural sciences Volterra integral equation 010104 statistics & probability symbols.namesake FOS: Mathematics Applied mathematics 0101 mathematics Representation (mathematics) Mathematics - Optimization and Control Equivalence (measure theory) ComputingMilieux_MISCELLANEOUS Mathematics Stochastic control Partial differential equation 0105 Mathematical Physics Probability (math.PR) 010102 general mathematics 0104 Statistics Probabilistic logic 16. Peace & justice [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Optimization and Control (math.OC) symbols Statistics Probability and Uncertainty Mathematics - Probability 60H20 35K58 60H30 |
| Zdroj: | Electronic Journal of Probability Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2021, 26 (89), pp.1-35. ⟨10.1214/21-EJP653⟩ Electronic Journal of Probability, 26 |
| ISSN: | 1083-6489 |
| DOI: | 10.1214/21-EJP653⟩ |
| Popis: | We study a novel general class of multidimensional type-I backward stochastic Volterra integral equations. Toward this goal, we introduce an infinite family of standard backward SDEs and establish its well-posedness, and we show that it is equivalent to that of a type-I backward stochastic Volterra integral equation. We also establish a representation formula in terms of non-linear semi-linear partial differential equation of Hamilton-Jacobi-Bellman type. As an application, we consider the study of time-inconsistent stochastic control from a game-theoretic point of view. We show the equivalence of two current approaches to this problem from both a probabilistic and an analytic point of view. ISSN:1083-6489 |
| Databáze: | OpenAIRE |
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