Many analysts argue that the Internet is producing a fundamental change in the way that business works. The network economy grows faster every day. Internet markets are developing rapidly with information being the single most traded commodity on the Internet. This paper looks at the extent to which conventional pricing theory applies to this type of good and whether it requires modifications i...

We tightly analyze the sample complexity of CCA, provide a learning algorithm that achieves optimal statistical performance in time linear in the required number of samples (up to log factors), as well as a streaming algorithm with similar guarantees.

Canonical correlation analysis (CCA) is a classical representation learning technique for finding correlated variables in multi-view data. Several nonlinear extensions of the original linear CCA have been proposed, including kernel and deep neural network methods. These approaches seek maximally correlated projections among families of functions, which the user specifies (by choosing a kernel o...

Given a bivariate distribution, the set of canonical correlations and functions is in general finite or countable. By using an inner product between two functions via an extension of the covariance, we find all the canonical correlations and functions for the so-called Cuadras-Augé copula and prove the continuous dimensionality of this distribution.

We consider the state price densities that are implicit in financial asset prices. In the pricing of an option, the state price density is proportional to the second derivative of the option pricing function and this relationship together with no arbitrage principle imposes restrictions on the pricing function such as monotonicity and convexity. Since the state price density is a proper density...

We consider asset price processes Xt which are weak solutions of onedimensional stochastic di erential equations of the form dXt = b(t; Xt) dt + t Xt dWt: Such price models can be interpreted as non{lognormally{distributed generalizations of the geometric Brownian motion. We study properties of the I divergence between the law of the solution Xt and the corresponding drift{less measure (the spe...

The following paper develops the basics behind stochastic calculus, which extends the theory of integration to stochastic (random) processes. The paper starts off with developing Brownian motion and its properties, which are used to develop the theory behind Itô integration. Several forms of the Itô integral are presented. A brief overview of the Radon-Nikodym and Girsanov Theorems are presente...

In this paper we present cluster canonical correlation analysis (cluster-CCA) for joint dimensionality reduction of two sets of data points. Unlike the standard pairwise correspondence between the data points, in our problem each set is partitioned into multiple clusters or classes, where the class labels define correspondences between the sets. Cluster-CCA is able to learn discriminant low dim...