This paper concerns the problems of quadratic hedging and pricing, and mean-variance portfolio selection in an incomplete market setting with continuous trading, multiple assets, and Brownian information. In particular, we assume throughout that the parameters describing the market model may be random processes. We approach these problems from the perspective of linear-quadratic (LQ) optimal co...

We present a technique for the rigorous computation of periodic orbits in certain ordinary differential equations. The method combines set oriented numerical techniques for the computation of invariant sets in dynamical systems with topological index arguments. It not only allows for the proof of existence of periodic orbits but also for a precise (and rigorous) approximation of these. As an ex...

Given a nite set of non-collinear points in the plane there exists a line that passes through exactly two points. Such a line is called an ordinary line. An e cient algorithm for computing such a line was proposed by Mukhopadhyay et al [MAH97]. In this note we extend this result in two directions. We rst show how to use this algorithm to compute an ordinary conic, that is, a conic passing throu...

The uniqueness has been proved by Piatetskiî-Sapiro and Safarevic. The proof of existence is outlined below. Let o be the closed point of A = Spec C[[t] ]. Let An be the finite covering of A obtained by extracting an nth. root of t; let on be the closed point of An. A family of surfaces over An is a flat, projective map ƒ: Xn —> An such that the generic fiber is smooth, connected, and two dimen...

We consider the cubic and quintic Gross-Pitaevskii (GP) hierarchies in d ≥ 1 dimensions, for focusing and defocusing interactions. We present a new proof of existence of solutions that does not require the a priori bound on the spacetime norm, which was introduced in the work of Klainerman and Machedon, [19], and used in our earlier work, [6].

In this survey, we review fundamental properties of coalgebras and their representation theory. Following J.A. Green we present the block theory of coalgebras using indecomposable injectives comodules. Using the cohom and cotensor functors we state Takeuchi-Morita equivalence and use it to sketch the proof of existence of “basic” coalgebras, due to the author and S. Montgomery. This leads to a ...

Abstract. The approach, referred to as ”monodromy transform”, provides some general base for solution of all known integrable space time symmetry reductions of Einstein equations for the case of pure vacuum gravitational fields, in the presence of gravitationally interacting massless fields, as well as for some string theory induced gravity models. In this communication we present the key point...

It is sometimes argued that possible worlds are too rich. Indeed, for every sentence φ and every world w, either φ is true at w, or ¬φ is true at w. Possible worlds leave nothing unsettled: for any question one may ask, there is always an answer, yes or no. My view goes along the opposite side. I take possible worlds to be incredibly poor, and I think that a good deal can be added to them. The ...