Related papers: Taylor approximation of incomplete Radner equilibr…
We prove the global existence of an incomplete, continuous-time finite-agent Radner equilibrium in which exponential agents optimize their expected utility over both running consumption and terminal wealth. The market consists of a traded…
In this article we consider the approximation of compact linear operators defined over tensor product Hilbert spaces. Necessary and sufficient conditions on the singular values of the problem under which we can or cannot achieve different…
We construct continuous-time equilibrium models based on a finite number of exponential utility investors. The investors' income rates as well as the stock's dividend rate are governed by discontinuous Levy processes. Our main result…
We consider M-estimators and derive supremal-inequalities of exponential-or polynomial type according as a boundedness- or a moment-condition is fulfilled. This enables us to derive rates of r-complete convergence and also to show r-qick…
We offer mathematical tractability and new insights for a framework of exponential utility with non-negative consumption, a constraint often omitted in the literature giving rise to economically unviable solutions. Specifically, using the…
We study the problem of convergence to equilibrium for evolution equations associated to general quadratic operators. Quadratic operators are non-selfadjoint differential operators with complex-valued quadratic symbols. Under appropriate…
We deduce a sufficient condition of the exponential (integral) turnpike property for infinite dimensional generalized linear-quadratic optimal control problems in terms of structural properties of the control system, such as exponential…
This note concerns a class of matrix Riccati equations associated with stochastic linear-quadratic optimal control problems with indefinite state and control weighting costs. A novel sufficient condition of solvability of such equations is…
We give a sufficient condition for the existence of a quadratic exponential vector with test function in L2(Rd) ? L?(Rd). We prove the linear independence and totality, in the quadratic Fock space, of these vectors. Using a technique…
We study a two-speed model with variant drift fields, which generalizes the Goldstein-Taylor model but the two advection fields are not necessarily in proportion. Due to the lack of a local equilibrium structure of the steady state,…
We give a collection of explicit sufficient conditions for the true martingale property of a wide class of exponentials of semimartingales. We express the conditions in terms of semimartingale characteristics. This turns out to be very…
The theory of nonlinear balanced truncation provides a system-theoretic framework for model reduction that preserves important properties such as stability, controllability, and observability. We present a scalable algorithm for computing…
We prove that in smooth Markovian continuous-time economies with potentially complete asset markets, Radner equilibria with endogenously complete markets exist.
We clarify how close a second order fully nonlinear equation can come to uniform ellipticity, through counting large eigenvalues of the linearized operator. This suggests an effective and novel way to understand the structure of fully…
The method of constructing approximate solutions of the first boundary value problem for linear differential equations based on incomplete (even and odd) trigonometric splines is considered. The theoretical positions are illustrated by…
This paper is devoted to discussing the weighted linear tensor product problems in the worst case setting. We consider algorithms that use finitely many evaluations of arbitrary continuous linear functionals. We investigate exponential $(s,…
First examples of quasi-exactly solvable models describing spin-orbital interaction are constructed. In contrast with other examples of matrix quasi-exactly solvable models discussed in the literature up to now, our models admit (but still…
The Riccati equations reducible to first-order linear equations by an appropriate change the dependent variable are singled out. All these equations are integrable by quadrature. A wide class of linear ordinary differential equations…
In the present article, we review a continual effort on generalization of the Trotter formula to higher-order exponential product formulas. The exponential product formula is a good and useful approximant, particularly because it conserves…
Motivated by an equilibrium problem, we establish the existence of a solution for a family of Markovian backward stochastic differential equations with quadratic nonlinearity and discontinuity in $Z$. Using unique continuation and backward…