2020
DOI: 10.1007/s11009-019-09764-y
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Discrete-type Approximations for Non-Markovian Optimal Stopping Problems: Part II

Abstract: In this paper, we present a Longstaff-Schwartz-type algorithm for optimal stopping time problems based on the Brownian motion filtration. The algorithm is based on Leão, Ohashi and Russo [30] and, in contrast to previous works, our methodology applies to optimal stopping problems for fully non-Markovian and non-semimartingale state processes such as functionals of pathdependent stochastic differential equations and fractional Brownian motions. Based on statistical learning theory techniques, we provide overall… Show more

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Cited by 5 publications
(20 citation statements)
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“…, e(k, T ) − 1, so that one can postulate max Z k 0 (0); U k 0 (0) as a possible approximation for (3.8). Having said that, we are now able to produce a Longstaff-Schwartz-type Monte-Carlo scheme as demonstrated by [7] which we briefly outline here. For further details, we refer the reader to [7].…”
Section: Non-markovian Sde Driven By Fractional Brownian Motionmentioning
confidence: 99%
See 3 more Smart Citations
“…, e(k, T ) − 1, so that one can postulate max Z k 0 (0); U k 0 (0) as a possible approximation for (3.8). Having said that, we are now able to produce a Longstaff-Schwartz-type Monte-Carlo scheme as demonstrated by [7] which we briefly outline here. For further details, we refer the reader to [7].…”
Section: Non-markovian Sde Driven By Fractional Brownian Motionmentioning
confidence: 99%
“…In order to compute a precise number of steps in our scheme, we just need to apply Propositions 5.1 and 5.3 combined with Corollary 4.1 in [7]. In this case, similar to the classical Markovian case, smoothness of the continuation values U k j ; j = 0, .…”
Section: Non-markovian Sde Driven By Fractional Brownian Motionmentioning
confidence: 99%
See 2 more Smart Citations
“…In [33], the authors show that a large class of Wiener functionals admits a stable imbedded discrete structure which has to be interpreted as a rather weak concept of continuity w.r.t Brownian motion driving noise. One major advantage of this theory is the possibility of computing the sensitivities of X w.r.t B via simple and explicit differential-type operators based on D. For a concrete application of this theory, we refer the reader to [34,35,5].…”
Section: Introductionmentioning
confidence: 99%