Explicit Bounds for the Distribution Function of the Sum of Dependent Normally Distributed Random Variables
Walter Schneider
TL;DR
This paper derives explicit bounds for the distribution function of the sum of dependent normal variables using copulas, providing a general approach without restricting the dependence structure, and illustrates the bounds numerically.
Contribution
It introduces a novel analytic method to bound the sum distribution of dependent normal variables without assuming a specific dependence type.
Findings
Derived explicit bounds for the sum distribution function.
Numerical illustrations demonstrate the bounds' effectiveness.
The approach is general, applicable to any dependence structure.
Abstract
In this paper an analytic expression is given for the bounds of the distribution function of the sum of dependent normally distributed random variables. Using the theory of copulas and the important Frechet bounds the dependence structure is not restricted to any specific type. Numerical illustrations are provided to assess the quality of the derived bounds.
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Taxonomy
TopicsFinancial Risk and Volatility Modeling · Probability and Risk Models · Stochastic processes and financial applications