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Journal Articles Journal of Applied Probability Year : 2019

Discrete-type approximations for non-Markovian optimal stopping problems: Part I

Abstract

Abstract 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 $\varepsilon$ -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 stochastic differential equations 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 et al .

Dates and versions

hal-04489379 , version 1 (05-03-2024)

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Dorival Leão, Alberto Ohashi, Francesco Russo. Discrete-type approximations for non-Markovian optimal stopping problems: Part I. Journal of Applied Probability, 2019, 56 (4), pp.981-1005. ⟨10.1017/jpr.2019.57⟩. ⟨hal-04489379⟩

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