Sharp Probability Tail Estimates for Portfolio Credit Risk

Autor: Jeffrey F. Collamore, Hasitha de Silva, Anand N. Vidyashankar

Publikováno v: Risks, Vol 10, Iss 12, p 239 (2022)

Portfolio credit risk is often concerned with the tail distribution of the total loss, defined to be the sum of default losses incurred from a collection of individual loans made out to the obligors. The default for an individual loan occurs when the

Externí odkaz: https://doaj.org/article/4b84006e929645bb87cf1d72bc2c1af2

Rare Event Analysis for Minimum Hellinger Distance Estimators via Large Deviation Theory

Autor: Jeffrey F. Collamore, Anand N. Vidyashankar

Publikováno v: Entropy
Entropy, Vol 23, Iss 386, p 386 (2021)
Vidyashankar, A N & Collamore, J F 2021, ' Rare event analysis for minimum Hellinger distance estimators via large deviation theory ', Entropy, vol. 23, no. 4, 386 . https://doi.org/10.3390/e23040386
Volume 23
Issue 4

Hellinger distance has been widely used to derive objective functions that are alternatives to maximum likelihood methods. While the asymptotic distributions of these estimators have been well investigated, the probabilities of rare events induced by

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::df9df3378b2fbde87cfad83b230b1281
http://europepmc.org/articles/PMC8064381

Large deviation estimates for exceedance times of perpetuity sequences and their dual processes

Autor: Dariusz Buraczewski, Ewa Damek, Jeffrey F. Collamore, Jacek Zienkiewicz

Publikováno v: Buraczewski, D, Collamore, J F, Damek, E & Zienkiewicz, J 2016, ' Large deviation estimates for exceedance times of perpetuity sequences and their dual processes ', Annals of Probability, vol. 44, no. 6, pp. 3688-3739. . https://doi.org/10.1214/15-AOP1059
Ann. Probab. 44, no. 6 (2016), 3688-3739

In a variety of problems in pure and applied probability, it is relevant to study the large exceedance probabilities of the perpetuity sequence $Y_{n}:=B_{1}+A_{1}B_{2}+\cdots+(A_{1}\cdots A_{n-1})B_{n}$, where $(A_{i},B_{i})\subset(0,\infty)\times\m

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::60729cd3e3809b19d1f1e4b442c45ca0
https://doi.org/10.1214/15-aop1059

Rare event simulation for processes generated via stochastic fixed point equations

Autor: Anand N. Vidyashankar, Guoqing Diao, Jeffrey F. Collamore

Publikováno v: Ann. Appl. Probab. 24, no. 5 (2014), 2143-2175
Collamore, J F, Diao, G & Vidyashankar, A N 2014, ' Rare event simulation for processes generated via stochastic fixed point equations ', Annals of Applied Probability, vol. 24, no. 5, pp. 2143-2175 . https://doi.org/10.1214/13-AAP974

In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable $V$ satisfying the distributional equation $V\stackrel{\mathcal{D}}{=}f(V)$, where $f(v)=A\

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3ad142234555581d13ac6da239907384
https://doi.org/10.1214/13-aap974

Tail estimates for stochastic fixed point equations via nonlinear renewal theory

Autor: Jeffrey F. Collamore, Anand N. Vidyashankar

Publikováno v: Collamore, J F & Vidyashankar, A N 2013, ' Tail estimates for stochastic fixed point equations via nonlinear renewal theory ', Stochastic Processes and Their Applications, vol. 123, no. 9, pp. 3378-3429 . https://doi.org/10.1016/j.spa.2013.04.015

This paper presents precise large deviation estimates for solutions to stochastic fixed point equations of the type V =_d f(V), where f(v) = Av + g(v) for a random function g(v) = o(v) a.s. as v tends to infinity. Specifically, we provide an explicit

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2912ffc3bfe48b7795a5ef8eb2f98358
https://curis.ku.dk/portal/da/publications/tail-estimates-for-stochastic-fixed-point-equations-via-nonlinear-renewal-theory(39bcbdef-f57e-4e92-a383-e6c70087b2c8).html