State-dependent importance sampling schemes via minimum cross-entropy

Abstract

We present a method to obtain state-and time-dependent importance sampling estimators by repeatedly solving a minimum cross-entropy (MCE) program as the simulation progresses. This MCE-based approach lends a foundation to the natural notion to stop changing the measure when it is no longer needed. We use this method to obtain a stateand time-dependent estimator for the one-tailed probability of a light-tailed i.i.d. sum that is logarithmically efficient in general and strongly efficient when the jumps are Gaussian. We go on to construct an estimator for the two-tailed problem which is shown to be similarly efficient. We consider minor variants of the algorithm obtained via MCE, and present some numerical comparisons between our algorithms and others from the literature.

Variance Reduction Techniques in Monte Carlo Methods

“…A cross-entropy minimization is applied after each state S k for determining the PDF of the next jump (Ridder and Taimre, 2009). The result is that when the level-crossing at time n can be reached from state S k just by following the natural drift, no change of measure is applied.…”

Vacation Model

“…2. A cross-entropy minimization is applied after each state S k for determining the PDF of the next jump (Ridder and Taimre 2011). The result is that when the level-crossing at time n can be reached from state S k just by following the natural drift, no change of measure is applied.…”

Variance Reduction Techniques in Monte Carlo Methods

“…(ii). A cross-entropy minimization is applied after each state S k for determining the PDF of the next jump (Ridder and Taimre, 2009). The result is that when the level-crossing at time n can be reached from state S k just by following the natural drift, no change of measure is applied.…”