Discrete-type approximations for non-Markovian optimal stopping problems: Part I
| Autor: | Dorival Leão, Francesco Russo, Alberto Ohashi |
|---|---|
| Přispěvatelé: | Unité de Mathématiques Appliquées (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA Paris), Optimisation et commande (OC), École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
General Mathematics Monte Carlo method Computational Finance (q-fin.CP) 01 natural sciences FOS: Economics and business 010104 statistics & probability Stochastic differential equation Quantitative Finance - Computational Finance 0502 economics and business Filtration (mathematics) FOS: Mathematics Applied mathematics Optimal stopping 0101 mathematics Brownian motion ComputingMilieux_MISCELLANEOUS Mathematics Stochastic control 050208 finance Fractional Brownian motion 05 social sciences Probability (math.PR) [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Variational inequality Statistics Probability and Uncertainty Mathematics - Probability |
| Zdroj: | Journal of Applied Probability Journal of Applied Probability, Cambridge University press, 2019, 56 (4), pp.981-1005. ⟨10.1017/jpr.2019.57⟩ |
| ISSN: | 0021-9002 1475-6072 |
| Popis: | In this paper, we present a discrete-type approximation scheme to solve continuous-time optimal stopping problems based on fully non-Markovian continuous processes adapted to the Brownian motion filtration. The approximations satisfy suitable variational inequalities which allow us to construct $\epsilon$-optimal stopping times and optimal values in full generality. Explicit rates of convergence are presented for optimal values based on reward functionals of path-dependent SDEs driven by fractional Brownian motion. In particular, the methodology allows us to design concrete Monte-Carlo schemes for non-Markovian optimal stopping time problems as demonstrated in the companion paper by Bezerra, Ohashi and Russo. Comment: Final version to appear in Journal of Applied Probability |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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