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Discrete-type approximations for non-Markovian optimal stopping problems: Part I
Ist Teil von
Journal of applied probability, 2019-12, Vol.56 (4), p.981-1005
Ort / Verlag
Cambridge University press
Erscheinungsjahr
2019
Link zum Volltext
Quelle
Alma/SFX Local Collection
Beschreibungen/Notizen
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 .