arXiv subjects

Ivar Ekeland

Publications and source records attributed to Ivar Ekeland.

21 records · Page 2Linked to original sources

arXiv2005

A theory of bond portfolios

We introduce a bond portfolio management theory based on foundations similar to those of stock portfolio management. A general continuous-time zero-coupon market is considered. The problem of optimal portfolios of zero-coupon bonds is solved for general utility functions, under a condition of no-arbitrage in the zero-coupon market. A mutual fund theorem is proved, in the case of deterministic volatilities. Explicit expressions are given for the optimal solutions for several utility functions.

math.OC↗

arXiv2003

An optimal matching problem

Given two measured spaces (X,dx), (Y,dy) and a third space Z, given two functions u(x,z) and v(x,z), we study the problem of finding two maps s from X to Z and t from Y to Z such that the images s(dx) and t(dy) coincide, and the integral of u(x,s(x))dx+v(y,t(y))dy is maximal. We give condition on u and v for which there is a unique solution.

math.OC↗

arXiv2003

A duality theory for some non-convex functions of matrices

We study a special class of non-convex functions which appear in nonlinear elasticity; and we prove that they have well-defined Legandre transforms. Several examples are given, and an application to a nonlinear eigenvalue problem

math.OC↗