Representation of non-Markovian optimal stopping problems by constrained BSDEs with a single jump
| Autor: | Marco Fuhrman, Federica Zeni, Huyên Pham |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
Mathematical optimization Optimization problem 010102 general mathematics Markov process randomized stopping 01 natural sciences Point process 010104 statistics & probability Stochastic differential equation symbols.namesake optimal stopping Integrator backward stochastic differential equations symbols Applied mathematics Optimal stopping 60H10 0101 mathematics Statistics Probability and Uncertainty Representation (mathematics) 60G40 Sign (mathematics) Mathematics |
| Zdroj: | Electron. Commun. Probab. |
| Popis: | We consider a non-Markovian optimal stopping problem on finite horizon. We prove that the value process can be represented by means of a backward stochastic differential equation (BSDE), defined on an enlarged probability space, containing a stochastic integral having a one-jump point process as integrator and an (unknown) process with a sign constraint as integrand. This provides an alternative representation with respect to the classical one given by a reflected BSDE. The connection between the two BSDEs is also clarified. Finally, we prove that the value of the optimal stopping problem is the same as the value of an auxiliary optimization problem where the intensity of the point process is controlled. |
| Databáze: | OpenAIRE |
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