Explicit form and robustness of martingale representations
成果类型：
Article
署名作者：
Jacod, J; Méléard, S; Protter, P
署名单位：
Sorbonne Universite; Universite Paris Nanterre; Purdue University System; Purdue University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
2000
页码：
1747-1780
关键词：
摘要：
Stochastic integral representation of martingales has been undergoing a renaissance due to questions motivated by stochastic finance theory. In the Brownian case one usually has formulas (of differing degrees of exactness) for the predictable integrands. We extend some of these to Markov cases where one does not necessarily have stochastic integral representation of all martingales. Moreover we study various convergence questions that arise naturally from (for example) approximations of price processes via Euler schemes for solutions of stochastic differential equations. We obtain general results of the following type: let U, U-n be random variables with decompositions U = alpha + integral (infinity)(0) xi (s) dX(s) +N-infinity, U-n = alpha (n) + integral (infinity)(0) xi (n)(s) dX(s)(n) + N-infinity(n), where X, N, X-n, N-n are martingales. If X-n --> X and U-n --> U, when and how does xi (n) --> xi?