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Discrete-type approximations for non-Markovian optimal stopping problems: Part II. (arXiv:1707.05250v1 [q-fin.CP])

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In this paper, we present a Longstaff-Schwartz-type algorithm for the discretization method designed in Le\~ao, Ohashi and Russo [28]. In contrast to previous works, our methodology applies to optimal stopping problems for fully non-Markovian and non-semimartingale state processes. Based on statistical learning theory techniques, we provide overall error estimates in terms of concrete approximation architecture spaces with finite Vapnik-Chervonenkis dimension. Analytical properties of continuation values for path-dependent SDEs and concrete linear architecture approximating spaces are also discussed.


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