A New Unbiased Stochastic Derivative Estimator for Discontinuous Sample Performances with Structural Parameters

Abstract

In this paper, we propose a new unbiased stochastic derivative estimator in a framework that can handle discontinuous sample performances with structural parameters. This work extends the three most popular unbiased stochastic derivative estimators: (1) infinitesimal perturbation analysis (IPA), (2) the likelihood ratio (LR) method, and (3) the weak derivative method, to a setting where they did not previously apply. Examples in probability constraints, control charts, and financial derivatives demonstrate the broad applicability of the proposed framework. The new estimator preserves the singlerun efficiency of the classic IPA-LR estimators in applications, which is substantiated by numerical experiments.

Maximum Likelihood Estimation by Monte Carlo Simulation: Toward Data-Driven Stochastic Modeling

“…For our main theoretical results, Theorem 1 presents the GLR estimator for the first-order distribution sensitivity with respect to z, which is a special case of the general setting in Peng et al (2018) under simpler conditions (A.1)-(A.3) enabled by an explicit construction of a smoothing sequence for the performance function that utilizes the specific structure of the indicator function. Theorem 2 extends the GLR estimator, for the first time, to any order of the distribution sensitivity.…”

“…The generalized likelihood ratio (GLR) method in Peng et al (2018) can deal with a larger scope of discontinuities in the sample performance. We use this technique to estimate the density and its derivatives, which fall under the umbrella of "distribution sensitivities"-derivatives of the distribution function with respect to (w.r.t.)…”

Indirect inference with a non-smooth criterion function

“…The HOPP method is a COV technique that allows the construction of unbiased estimators, up to a third-order term, for the derivatives of certain expectations that are of keen interest in financial mathematics, such as the so-called "Greeks" that are associated with option pricing. Additional COV strategies for calculating derivatives of similar expectations can be found in Fu (1994), Lyuu and Teng (2011), Chan and Joshi (2011) and Peng et al (2018), with these ideas first introduced by Glynn (1987) in the study of discrete-event systems. 1 Unlike the problems to which the HOPP method is applied, which focuses on estimating derivatives of an expectation at a point, in II we are interested in obtaining uniformly, over the parameter space, consistent estimates for the derivatives of a simulated sample criterion function.…”

On gamma estimation via matrix kriging

“…However, its estimators typically have larger variances than those of the pathwise method. As improvements and complements of the pathwise and the likelihood ratio method, some other methods, for example, kernel method (Elie, Fermanian, & Touzi, ; Liu & Hong, ), weak derivatives method (Heidergott, Vazquez‐Abad, Pflug, & Farenhorst‐Yuan, ; Pflug, ), and generalized likelihood ratio method (Peng, Fu, Hu, & Heidergott, ; Wang, Fu, & Marcus, ) are proposed.…”