We extend a result of Dubins (1975) from bounded to unbounded random variables. Dubins (1975) showed that a finitely additive expectation over the collection of bounded random variables can be written as an integral of conditional expectations (disintegrability) if and only if the marginal expectation is always within the smallest closed interval containing the conditional expectations (conglom...

The paper derives saddlepoint expansions for conditional expectations in the form of E[X |Y = a] and E[X|Y ≥ a] for the sample mean of a continuous random vector (X,Y) whose joint moment generating function is available. Theses conditional expectations frequently appear in various applications, particularly in quantitative finance and risk management. Using the newly developed saddlepoint expan...

We extend a result of Dubins (Ann Probab 3:89–99, 1975) from bounded to unbounded random variables. Dubins showed that a finitely additive expectation over the collection of bounded random variables can be written as an integral of conditional expectations (disintegrability) if and only if the marginal expectation is always within the smallest closed interval containing the conditional expectat...

Abstract We introduce a novel regression model for the conditional left and right tail of possibly heavy-tailed response. The proposed can be used to learn effect covariates on an extreme value setting via Lasso-type specification based Lagrangian restriction. Our track if some are significant lower values, but not (right) tail—and vice versa; in addition this, bypasses need threshold selection...

Conditional value at risk (CVaR) is a popular measure for quantifying portfolio risk. Sensitivity analysis of CVaR common in management and gradient-based optimization algorithms. In this paper, we study the infinitesimal perturbation estimator sensitivity using randomized quasi-Monte Carlo (RQMC) simulation. RQMC has proved valuable financial option pricing with better rate convergence compare...

The purpose of regression analysis is to expose the relationship between a response variable and predictor variables. In real applications, the response variable cannot be predicted exactly from the predictor variables. Instead, the response for a fixed value of each predictor variable is a random variable. For this reason, we often summarize the behavior of the response for fixed values of the...

we prove that the limit of a sequence of pettis integrable bounded scalarly measurable weak random elements, of finite weak norm, with values in the dual of a non-separable banach space is pettis integrable. then we provide basic properties for the pettis conditional expectation, and prove that it is continuous. calculus of pettis conditional expectations in general is very different from the c...

The ν-support vector classification (ν-SVC) algorithm was shown to work well and provide intuitive interpretations, e.g., the parameter ν roughly specifies the fraction of support vectors. Although ν corresponds to a fraction, it cannot take the entire range between 0 and 1 in its original form. This problem was settled by a non-convex extension of ν-SVC and the extended method was experimental...