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Approximating random variables by stochastic integrals. (English) Zbl 0814.60041

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.

MSC:

60G48 Generalizations of martingales
60H05 Stochastic integrals
91G20 Derivative securities (option pricing, hedging, etc.)
60H30 Applications of stochastic analysis (to PDEs, etc.)
90C20 Quadratic programming
91G80 Financial applications of other theories
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