Randomly weighted sums of subexponential random variables with application to capital allocation

Qihe Tang; Zhongyi Yuan

doi:10.1007/s10687-014-0191-z

Randomly weighted sums of subexponential random variables with application to capital allocation

Qihe Tang, Zhongyi Yuan

Risk Management

Research output: Contribution to journal › Article › peer-review

77 Scopus citations

Abstract

We are interested in the tail behavior of the randomly weighted sum ∑_i=1 ⁿ θ_i X_i, in which the primary random variables X₁, …, X_n are real valued, independent and subexponentially distributed, while the random weights θ₁, …, θ_n are nonnegative and arbitrarily dependent, but independent of X₁, …, X_n. For various important cases, we prove that the tail probability of ∑_i=1 ⁿ θ_iX_i is asymptotically equivalent to the sum of the tail probabilities of θ₁X₁, …, θ_nX_n, which complies with the principle of a single big jump. An application to capital allocation is proposed.

Original language	English (US)
Pages (from-to)	467-493
Number of pages	27
Journal	Extremes
Volume	17
Issue number	3
DOIs	https://doi.org/10.1007/s10687-014-0191-z
State	Published - Sep 1 2014

All Science Journal Classification (ASJC) codes

Statistics and Probability
Engineering (miscellaneous)
Economics, Econometrics and Finance (miscellaneous)

Access to Document

10.1007/s10687-014-0191-z

Cite this

@article{e094d022bbe243f68abcd4e7d9d074a3,

title = "Randomly weighted sums of subexponential random variables with application to capital allocation",

abstract = "We are interested in the tail behavior of the randomly weighted sum ∑i=1 n θi Xi, in which the primary random variables X1, …, Xn are real valued, independent and subexponentially distributed, while the random weights θ1, …, θn are nonnegative and arbitrarily dependent, but independent of X1, …, Xn. For various important cases, we prove that the tail probability of ∑i=1 n θiXi is asymptotically equivalent to the sum of the tail probabilities of θ1X1, …, θnXn, which complies with the principle of a single big jump. An application to capital allocation is proposed.",

author = "Qihe Tang and Zhongyi Yuan",

note = "Publisher Copyright: {\textcopyright} 2014, Springer Science+Business Media New York.",

year = "2014",

month = sep,

day = "1",

doi = "10.1007/s10687-014-0191-z",

language = "English (US)",

volume = "17",

pages = "467--493",

journal = "Extremes",

issn = "1386-1999",

publisher = "Springer Netherlands",

number = "3",

}

TY - JOUR

T1 - Randomly weighted sums of subexponential random variables with application to capital allocation

AU - Tang, Qihe

AU - Yuan, Zhongyi

PY - 2014/9/1

Y1 - 2014/9/1

N2 - We are interested in the tail behavior of the randomly weighted sum ∑i=1 n θi Xi, in which the primary random variables X1, …, Xn are real valued, independent and subexponentially distributed, while the random weights θ1, …, θn are nonnegative and arbitrarily dependent, but independent of X1, …, Xn. For various important cases, we prove that the tail probability of ∑i=1 n θiXi is asymptotically equivalent to the sum of the tail probabilities of θ1X1, …, θnXn, which complies with the principle of a single big jump. An application to capital allocation is proposed.

AB - We are interested in the tail behavior of the randomly weighted sum ∑i=1 n θi Xi, in which the primary random variables X1, …, Xn are real valued, independent and subexponentially distributed, while the random weights θ1, …, θn are nonnegative and arbitrarily dependent, but independent of X1, …, Xn. For various important cases, we prove that the tail probability of ∑i=1 n θiXi is asymptotically equivalent to the sum of the tail probabilities of θ1X1, …, θnXn, which complies with the principle of a single big jump. An application to capital allocation is proposed.

UR - http://www.scopus.com/inward/record.url?scp=84957428639&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84957428639&partnerID=8YFLogxK

U2 - 10.1007/s10687-014-0191-z

DO - 10.1007/s10687-014-0191-z

M3 - Article

AN - SCOPUS:84957428639

SN - 1386-1999

VL - 17

SP - 467

EP - 493

JO - Extremes

JF - Extremes

IS - 3

ER -

Randomly weighted sums of subexponential random variables with application to capital allocation

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this