APPROXIMATING RANDOM-VARIABLES BY STOCHASTIC INTEGRALS

• 成果类型: Article
• 署名作者: SCHWEIZER, M
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176988611
• 发表日期: 1994
• 页码: 1536-1575
• 关键词: martingale; portfolio; MARKET

摘要

Let X be a semimartingale and Theta the space of all predictable X-integrable processes theta such that integral theta dX is in the space S-2 of semimartingales, we consider the problem of approximating a given random variable H epsilon L(2) by a stochastic integral integral(0)(T) theta(s) dX(s), with respect to the L(2)-norm. If X is special and has the form X = X(0) +M+ integral alpha d(M), we construct a solution in feedback form under the assumptions that integral alpha(2)d(M) is deterministic and that H admits a strong F-S decomposition Into a constant, a stochastic integral of X and a martingale part orthogonal to M. We provide sufficient conditions for the existence of such a decomposition, and we give several applications to quadratic optimization problems arising in financial mathematics.