Approximating random variables by stochastic integrals (Q1345608)

This paper considers the problem of approximating in quadratic norm a given square-integrable random variable \(H\) by a given constant \(c\) and the stochastic integral of a predictable process with respect to some given special semimartingale \(X\), under some assumptions on the canonical decomposition of \(X\). If \(H\) admits a decomposition into a constant, a stochastic integral with respect to \(X\) and the terminal value of a martingale orthogonal to the martingale part of \(X\), then there is a solution for every real number \(c\), and this solution is explicitly given in a feedback form. Several applications are given to quadratic optimization problems arising in financial mathematics.