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

Author

Listed:
  • Aurélien Alfonsi

    (Ecole des Ponts, Marne-la-Vallée
    MathRisk, Inria)

  • Bernard Lapeyre

    (Ecole des Ponts, Marne-la-Vallée
    MathRisk, Inria)

  • Jérôme Lelong

    (Univ. Grenoble Alpes, CNRS, Grenoble INP, LJK)

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.

Suggested Citation

  • Aurélien Alfonsi & Bernard Lapeyre & Jérôme Lelong, 2023. "How Many Inner Simulations to Compute Conditional Expectations with Least-square Monte Carlo?," Methodology and Computing in Applied Probability, Springer, vol. 25(3), pages 1-25, September.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:3:d:10.1007_s11009-023-10038-x
    DOI: 10.1007/s11009-023-10038-x
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    References listed on IDEAS

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