This gives us a new probability measure on (Ω,F), so we may define expectations with respect to this conditioned probability measure. Thus for F measurable Y : Ω → R we define the conditional expectation E[Y | X = x] by taking the expectation of Y with respect to the measure (1.1). Consider now how to generalize the idea of conditional probability to the case when P (X = x) = 0. We wish to do t...

Estimators for the price of a discrete barrier option based on conditional expectation and importance sampling variance reduction techniques are given. There are erroneous formulas for the conditional expectation estimator published in the literature: we derive the correct expression for the estimator. We use a simulated annealing algorithm to estimate the optimal parameters of exponential twis...

Based on recent developments in joint regression models for quantile and expected shortfall, this paper seeks to develop analyse the risk right tail of distribution non-negative dependent random variables. We propose an algorithm estimate conditional expectation regressions, introducing generalized with link functions that are similar those linear models. To preserve natural ordering measures a...