How Many Inner Simulations to Compute Conditional Expectations with Least-square Monte Carlo?

Aurélien Alfonsi (), Bernard Lapeyre () and Jérôme Lelong ()
Additional contact information
Aurélien Alfonsi: Ecole des Ponts, Marne-la-Vallée
Bernard Lapeyre: Ecole des Ponts, Marne-la-Vallée
Jérôme Lelong: Univ. Grenoble Alpes, CNRS, Grenoble INP, LJK

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 3, 1-25

Abstract: Abstract The problem of computing the conditional expectation $${\mathbb E}[f(Y)|X]$$ E [ f ( Y ) | X ] with least-square Monte-Carlo is of general importance and has been widely studied. To solve this problem, it is usually assumed that one has as many samples of Y as of X. However, when samples are generated by computer simulation and the conditional law of Y given X can be simulated, it may be relevant to sample $$K\in {\mathbb N}$$ K ∈ N values of Y for each sample of X. The present work determines the optimal value of K for a given computational budget, as well as a way to estimate it. The main take away message is that the computational gain can be all the more important as the computational cost of sampling Y given X is small with respect to the computational cost of sampling X. Numerical illustrations on the optimal choice of K and on the computational gain are given on different examples including one inspired by risk management.

Keywords: Least square Monte-Carlo; Conditional expectation estimators; Variance reduction; 65C05; 91G60 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-023-10038-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:25:y:2023:i:3:d:10.1007_s11009-023-10038-x

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-023-10038-x

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().