MINIMAL SUPERSOLUTIONS OF CONVEX BSDES

• 成果类型: Article
• 署名作者: Drapeau, Samuel; Heyne, Gregor; Kupper, Michael
• 署名单位: Humboldt University of Berlin
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/13-AOP834
• 发表日期: 2013
• 页码: 3973-4001
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; g-brownian motion; Risk measures; calculus; THEOREM

摘要

We study the nonlinear operator of mapping the terminal value xi to the corresponding minimal supersolution of a backward stochastic differential equation with the generator being monotone in y, convex in z, jointly lower semicontinuous and bounded below by an affine function of the control variable z. We show existence, uniqueness, monotone convergence, Fatou's lemma and lower semicontinuity of this operator. We provide a comparison principle for minimal supersolutions of BSDEs.