On a generalized optional decomposition theorem

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2014-10-24 DOI:10.1080/17442508.2014.895357

A. Berkaoui

引用次数: 3

Abstract

First we consider a set of probabilities and denote by , the associated dynamic sublinear expectation, defined by for and a fixed filtration . We prove that for a positive -supermartingale X, there exits an increasing adapted process C such that is a local -martingale. Second we apply such a result to incomplete market under model misspecification, generalizing the results of Kramkov [D.O. Kramkov, Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets, Prob. Theor. Relat. Field. 15 (1996), pp. 459–479] and Riedel [F. Riedel, On optimal stopping under Ambiguity, Econometrica. 77 (2009), pp. 857–908].

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关于一个广义可选分解定理

首先，我们考虑一组概率，并表示，相关的动态次线性期望，定义为和一个固定的过滤。我们证明了对于一个正的-上鞅X，存在一个递增适应过程C，使得它是一个局部-鞅。其次，我们将此结果应用于模型不规范下的不完全市场，推广了Kramkov [D.O.]的结果《不完全证券市场上超鞅的可选分解与或有债权的套期保值》，vol . 11;定理。遗传代数。田展，15(1996)，第459-479页。Riedel，关于模糊情况下的最优停止，计量经济学，77 (2009)，pp. 857-908。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Stochastics-An International Journal of Probability and Stochastic Processes MATHEMATICS, APPLIED-STATISTICS & PROBABILITY

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Stochastics: An International Journal of Probability and Stochastic Processes is a world-leading journal publishing research concerned with stochastic processes and their applications in the modelling, analysis and optimization of stochastic systems, i.e. processes characterized both by temporal or spatial evolution and by the presence of random effects. Articles are published dealing with all aspects of stochastic systems analysis, characterization problems, stochastic modelling and identification, optimization, filtering and control and with related questions in the theory of stochastic processes. The journal also solicits papers dealing with significant applications of stochastic process theory to problems in engineering systems, the physical and life sciences, economics and other areas. Proposals for special issues in cutting-edge areas are welcome and should be directed to the Editor-in-Chief who will review accordingly. In recent years there has been a growing interaction between current research in probability theory and problems in stochastic systems. The objective of Stochastics is to encourage this trend, promoting an awareness of the latest theoretical developments on the one hand and of mathematical problems arising in applications on the other.