This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general enough to include cases in which no minimum exists, as occurs typically, for instance, with standard boosting algorithms. Concretely, we first show that any...

Empirical evidence shows that entrepreneurs hold a large fraction of wealth, have higher saving rates than workers, and face substantial uninsurable entrepreneurial and investment risks. This paper constructs a heterogeneous-agent general equilibrium model with uninsurable entrepreneurial risk and capital-market imperfections to explore the implications of uninsurable entrepreneurial risk for w...

Let (X ,μ) be a probability space, set X to be distributed according to μ and put Y to be an unknown target random variable. In the usual setup in learning theory, one observes N independent couples (Xi, Yi)Ni=1 in X × R, distributed according to the joint distribution of X and Y . The goal is to construct a real-valued function f which is a good guess/prediction of Y . A standard way of measur...

prediction of supersolubility and the width of the metastable zone has been a major concern among the workers in the field of industrial crystallization. operation of crystallizers under the optimum supersaturation low enough to attain the desired product quality (median particle size, crystal size distribution (csd), shape, purity) being one motif. the inherent relationship between the subject...

There are a number of techniques available to estimate saturated-liquid molar or specific volumes or densities of liquids. In this study, a new empirical correlation is presented to calculate volume of saturated liquids as a function of critical volume, reduced temperature and acentric factor. An optimization algorithm is utilized to obtain unknown parameters of this correlation by fitting them...

This paper addresses the gap between the theoretically well-understood impact of systematic risk on the loss-distribution of a credit-risky loan portfolio and the lack of empirical estimates of the default correlation. To this purpose we start with a one-factor model in which the correlation with the systematic risk factor equals the asset correlation between two firms. In the theoretical part ...

This empirical paper addresses the gap between the theoretically well-understood impact of systematic risk on the loss-distribution of a credit-risky loan portfolio and the lack of empirical estimates of the default correlation. To this purpose we start with a one-factor model in which the correlation with the systematic risk factor equals the asset correlation between two firms. The asset corr...

Suppose that {Xjk, j = 1, · · · , p1; k = 1, · · · , n} are independent and identically distributed (i.i.d) real random variables with EX11 = 0 and EX 2 11 = 1, and that {Yjk, j = 1, · · · , p2; k = 1, · · · , n} are i.i.d real random variables with EY11 = 0 and EY 2 11 = 1, and that {Xjk, j = 1, · · · , p1; k = 1, · · · , n} are independent of {Yjk, j = 1, · · · , p2; k = 1, · · · , n}. This p...