Approximating the Sum of Correlated Lognormals: An Implementation

Christopher J. Rook, M. Kerman
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引用次数: 5

Abstract

Lognormal random variables appear naturally in many engineering disciplines, including wireless communications, reliability theory, and finance. So, too, does the sum of (correlated) lognormal random variables. Unfortunately, no closed form probability distribution exists for such a sum, and it requires approximation. Some approximation methods date back over 80 years and most take one of two approaches, either: 1) an approximate probability distribution is derived mathematically, or 2) the sum is approximated by a single lognormal random variable. In this research, we take the latter approach and review a fairly recent approximation procedure proposed by Mehta, Wu, Molisch, and Zhang (2007), then implement it using C++. The result is applied to a discrete time model commonly encountered within the field of financial economics.
近似相关对数法的和:一个实现
对数正态随机变量自然地出现在许多工程学科中,包括无线通信、可靠性理论和金融。(相关的)对数正态随机变量的和也是如此。不幸的是,这种和不存在封闭形式的概率分布,它需要近似。一些近似方法可以追溯到80多年前,大多数采用两种方法中的一种:1)从数学上推导出近似概率分布,或者2)用单个对数正态随机变量近似求和。在本研究中,我们采用后一种方法,并回顾了Mehta、Wu、Molisch和Zhang(2007)最近提出的一种近似过程,然后使用c++实现它。结果应用于金融经济学领域中经常遇到的离散时间模型。
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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