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CONVERGENCE OF A LEAST‐SQUARES MONTE CARLO ALGORITHM FOR AMERICAN OPTION PRICING WITH DEPENDENT SAMPLE DATA
Author(s) -
Zanger Daniel Z.
Publication year - 2018
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12125
Subject(s) - monte carlo method , dimension (graph theory) , convergence (economics) , bounded function , mathematics , quasi monte carlo method , stochastic approximation , sample (material) , set (abstract data type) , nonlinear system , approximation error , regular polygon , mathematical optimization , algorithm , computer science , hybrid monte carlo , markov chain monte carlo , statistics , combinatorics , computer security , economic growth , mathematical analysis , chemistry , key (lock) , geometry , chromatography , quantum mechanics , programming language , physics , economics
We analyze the convergence of the Longstaff–Schwartz algorithm relying on only a single set of independent Monte Carlo sample paths that is repeatedly reused for all exercise time‐steps. We prove new estimates on the stochastic component of the error of this algorithm whenever the approximation architecture is any uniformly bounded set of L 2 functions of finite Vapnik–Chervonenkis dimension (VC‐dimension), but in particular need not necessarily be either convex or closed. We also establish new overall error estimates, incorporating bounds on the approximation error as well, for certain nonlinear, nonconvex sets of neural networks.