Work

Optimal distributions for randomized unbiased estimators with an infinite horizon and an adaptive algorithm

Year: 2025

Type: article

Abstract: The randomized unbiased estimators of Rhee & Glynn (2015, Unbiased estimation with square root convergence for SDE models. Oper. Res, 63, 1026–1043) can be highly efficient at approximating expectations of path functionals associated with stochastic differential equations. However, algorithms for calculating the optimal distributions with an infinite horizon are lacking. In this article, based on the method of Cui et al. (2021, On the optimal design of the randomized unbiased Monte Carlo estimators. Oper. Res. Lett., 49, 477–484), we prove that, under mild assumptions, there is a simple representation of the optimal distributions. Then, we develop an adaptive algorithm to compute the optimal distributions with an infinite horizon, which requires only a small amount of computational time in prior estimation. Finally, we provide numerical results to illustrate the efficiency of our adaptive algorithm.

Source: IMA Journal of Numerical Analysis

DOI: 10.1093/imanum/draf017

Authors: Chao Zheng, Jiangtao Pan, Qun Wang

Institution: Zhejiang University of Finance and Economics

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Awards: G1567583127, G4789400062