Random recurrence equations and ruin in a Markov-dependent stochastic economic environment

Research output: Contribution to journalJournal articlepeer-review

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Random recurrence equations and ruin in a Markov-dependent stochastic economic environment. / Collamore, Jeffrey F.

In: Annals of Applied Probability, Vol. 19, No. 4, 2009, p. 1404-1458.

Research output: Contribution to journalJournal articlepeer-review

Harvard

Collamore, JF 2009, 'Random recurrence equations and ruin in a Markov-dependent stochastic economic environment', Annals of Applied Probability, vol. 19, no. 4, pp. 1404-1458.

APA

Collamore, J. F. (2009). Random recurrence equations and ruin in a Markov-dependent stochastic economic environment. Annals of Applied Probability, 19(4), 1404-1458.

Vancouver

Collamore JF. Random recurrence equations and ruin in a Markov-dependent stochastic economic environment. Annals of Applied Probability. 2009;19(4):1404-1458.

Author

Collamore, Jeffrey F. / Random recurrence equations and ruin in a Markov-dependent stochastic economic environment. In: Annals of Applied Probability. 2009 ; Vol. 19, No. 4. pp. 1404-1458.

Bibtex

@article{50e459d0960c11de8bc9000ea68e967b,
title = "Random recurrence equations and ruin in a Markov-dependent stochastic economic environment",
abstract = "We develop sharp large deviation asymptotics for the probability of ruin in a Markov-dependent stochastic economic environment and study the extremes for some related Markovian processes which arise in financial and insurance mathematics, related to perpetuities and the ARCH(1) and GARCH(1,1) time series models.  Our results build upon work of Goldie, who has developed tail asymptotics applicable for independent sequences of random variables subject to a random recurrence equation.  In contrast, we adopt a general approach based on the theory of Harris recurrent Markov chains and the associated theory of nonnegative operators, and meanwhile develop certain recurrence properties for these operators under a nonstandart {"}Gartner-Ellis{"} assumption on the driving process.",
author = "Collamore, {Jeffrey F.}",
year = "2009",
language = "English",
volume = "19",
pages = "1404--1458",
journal = "Annals of Applied Probability",
issn = "1050-5164",
publisher = "Institute of Mathematical Statistics",
number = "4",

}

RIS

TY - JOUR

T1 - Random recurrence equations and ruin in a Markov-dependent stochastic economic environment

AU - Collamore, Jeffrey F.

PY - 2009

Y1 - 2009

N2 - We develop sharp large deviation asymptotics for the probability of ruin in a Markov-dependent stochastic economic environment and study the extremes for some related Markovian processes which arise in financial and insurance mathematics, related to perpetuities and the ARCH(1) and GARCH(1,1) time series models.  Our results build upon work of Goldie, who has developed tail asymptotics applicable for independent sequences of random variables subject to a random recurrence equation.  In contrast, we adopt a general approach based on the theory of Harris recurrent Markov chains and the associated theory of nonnegative operators, and meanwhile develop certain recurrence properties for these operators under a nonstandart "Gartner-Ellis" assumption on the driving process.

AB - We develop sharp large deviation asymptotics for the probability of ruin in a Markov-dependent stochastic economic environment and study the extremes for some related Markovian processes which arise in financial and insurance mathematics, related to perpetuities and the ARCH(1) and GARCH(1,1) time series models.  Our results build upon work of Goldie, who has developed tail asymptotics applicable for independent sequences of random variables subject to a random recurrence equation.  In contrast, we adopt a general approach based on the theory of Harris recurrent Markov chains and the associated theory of nonnegative operators, and meanwhile develop certain recurrence properties for these operators under a nonstandart "Gartner-Ellis" assumption on the driving process.

M3 - Journal article

VL - 19

SP - 1404

EP - 1458

JO - Annals of Applied Probability

JF - Annals of Applied Probability

SN - 1050-5164

IS - 4

ER -

ID: 14093053