完全和不完全离散时间市场模型的统计不可区分性

IF 1.4 Q3 SOCIAL SCIENCES, MATHEMATICAL METHODS

Decisions in Economics and Finance Pub Date : 2023-05-12 DOI:10.1007/s10203-023-00397-y

Nikolai Dokuchaev

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引用次数: 1

摘要

本文研究了随机离散时间股票市场模型的资产定价问题。研究了市场完备性统计评价的可能性。众所周知，市场完备性不是一个鲁棒性:系数的小随机偏差会使一个完全市场模型变成一个不完全市场模型。本文研究了市场不完备性是否具有鲁棒性。发现市场不完备性也是一个非鲁棒性。用一个基本的单股随机市场模型证明了这一点。这意味着，对于任何不完全市场，从广泛的离散时间模型，存在一个完整的市场模型，任意接近的股票价格。这意味着在市场统计上，不完全市场与完全市场是无法区分的。

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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On statistical indistinguishability of complete and incomplete discrete time market models

The paper studies asset pricing for stochastic discrete time stock market models. The possibility of statistical evaluation of the market completeness is investigated. It is known that the market completeness is not a robust property: small random deviations of the coefficients convert a complete market model into a incomplete one. The paper investigates if market incompleteness is robust. It is found that market incompleteness is a non-robust property as well. This is demonstrated for a basic single stock stochastic market model. This implies that, for any incomplete market from a wide class of discrete time models, there exists a complete market model with arbitrarily close stock prices. This means that incomplete markets are indistinguishable from the complete markets in the terms of market statistics.

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来源期刊

Decisions in Economics and Finance SOCIAL SCIENCES, MATHEMATICAL METHODS-

CiteScore

2.50

自引率

9.10%

发文量

期刊介绍： Decisions in Economics and Finance: A Journal of Applied Mathematics is the official publication of the Association for Mathematics Applied to Social and Economic Sciences (AMASES). It provides a specialised forum for the publication of research in all areas of mathematics as applied to economics, finance, insurance, management and social sciences. Primary emphasis is placed on original research concerning topics in mathematics or computational techniques which are explicitly motivated by or contribute to the analysis of economic or financial problems.