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Convergence of sums of dependent Bernoulli random variables: an application from portfolio theory

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  • Madelyn Houser
  • Pak-Wing Fok

Abstract

Generalizations of the Central Limit Theorem to N dependent random variables often assume that the dependence falls off as N→∞. In this paper we present an example from mathematical finance where convergence is independent of N. Specifically, we consider N≫1 dependent Bernoulli variates that represent N loans and probabilistic dependence among loans is based on an underlying economic model for default. A simple model for correlated default is the Vasicek Asymptotic Single Risk Factor (ASRF) framework. Our results showcase an example of “fast” convergence of dependent variates to this limiting non normal distribution with rate O(N−1).

Suggested Citation

  • Madelyn Houser & Pak-Wing Fok, 2019. "Convergence of sums of dependent Bernoulli random variables: an application from portfolio theory," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(23), pages 5673-5681, December.
    • Handle: RePEc:taf:lstaxx:v:48:y:2019:i:23:p:5673-5681
    DOI: 10.1080/03610926.2018.1517891
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