Asymptotic synthesis of contingent claims with controlled risk in a sequence of discrete-time markets

• 成果类型: Article
• 署名作者: Kreps, David M.; Schachermayer, Walter
• 署名单位: Stanford University; University of Vienna
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1933-6837
• DOI: 10.3982/TE4034
• 发表日期: 2021-01-01
• 页码: 25-47
• 关键词: Market completeness; Black-Scholes-Merton model; synthesis of contingent claims

摘要

We examine the connection between discrete-time models of financial markets and the celebrated Black-Scholes-Merton (BSM) continuous-time model in which markets are complete. Suppose that (a) the probability law of a sequence of discrete-time models converges to the law of the BSM model and (b) the largest possible one-period step in the discrete-time models converges to zero. We prove that, under these assumptions, every bounded and continuous contingent claim can be asymptotically synthesized, controlling for the risks taken in a manner that implies, for instance, that an expected-utility-maximizing consumer can asymptotically obtain as much utility in the (possibly incomplete) discrete-time economies as she can at the continuous-time limit. Hence, in economically significant ways, many discrete-time models with frequent trading resemble the complete-markets model of BSM.