Collaborative Research: Economics of Continuous Trading

合作研究：持续交易的经济学

• 批准号: 9710433
• 负责人: William Zame
• 金额: $ 19.41万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9710433&HistoricalAwards=false
• 关键词: Collaborative; Research; Economics; Continuous; Trading

Continuous trading models have been the central tools in modern financial theory ever since they were used to establish the Black-Scholes formula for correctly pricing options. Unfortunately, the continuous trading models rest on economic foundations that can be questioned. The object of this project is to put continuous trading models on a sounder economic footing. The most fundamental difficulty addressed is the meaning of continuous trading. The `obvious` interpretation of continuous trading is as a limit of models in which trading occurs at a finite number of discrete times, but the interval between trading times becomes very short. It can be argued on the basis of counter examples, that there is a serious economic difficulty with this interpretation. The aim of this research is to seek a more satisfactory interpretation. The second set of difficulties addressed concerns the nature and existence of equilibrium. Most of the analysis of continuous trading models is non-equilibrium in nature; for example, the Black-Scholes analysis takes the process describing security prices as given and solves for option prices by arbitrage arguments. Other analyses simply assume the existence of a suitable equilibrium. From an economic point of view, assuming the existence of such an equilibrium is generally unsatisfactory. It is particularly unsatisfactory in the continuous time setting because the existence of equilibrium is very much in doubt in many cases of interest, and because even when the existence of an equilibrium satisfying regularity conditions is guaranteed, there may be many other equilibria. This research will seek to establish the existence of equilibrium and to rule out equilibria not satisfying regularity conditions.

自连续交易模型被用来建立正确定价期权的布莱克-斯科尔斯公式以来，它一直是现代金融理论的核心工具。不幸的是，持续交易模式所依赖的经济基础是可以被质疑的。该项目的目的是将连续交易模式建立在更健全的经济基础上。最根本的困难是持续交易的意义。对连续交易的“明显”解释是，交易在有限的离散时间内发生，但交易时间之间的间隔变得非常短。在反例的基础上，可以认为这种解释存在严重的经济困难。本研究的目的是寻求一个更令人满意的解释。讨论的第二组困难涉及平衡的性质和存在。大多数连续交易模型的分析本质上是非均衡的；例如，Black-Scholes分析将描述证券价格的过程视为给定，并通过套利论证来解决期权价格问题。其他的分析只是假设存在一个适当的平衡。从经济学的观点来看，假设存在这样一种均衡通常是不令人满意的。在连续时间条件下，它尤其不能令人满意，因为在许多情况下，平衡的存在是非常令人怀疑的，因为即使保证存在满足正则性条件的平衡，也可能存在许多其他平衡。本研究将寻求建立平衡的存在，并排除不满足规则条件的平衡。