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

By Jeffrey F. Collamore. 2009

47 citations recorded by the source corpus.

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 $\operatorname {ARCH}(1)$ and $\operatorname {GARCH}(1,1)$ time series models. Our results build upon work of Goldie [Ann. Appl. Probab. 1 (1991) 126--166], 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 nonstandard "G\"artner--Ellis" assumption on the driving process.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/01d55979aa178f1fd8202021121dafbef866cec2

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In Finance

1. Jostein Paulsen
2. Qihe Tang
3. Kam Chuen Yuen
4. Claudia Klüppelberg
5. Radostina Kostadinova

In Management Science and Operations Research

1. Jostein Paulsen
2. Qihe Tang
3. Kam Chuen Yuen
4. Radostina Kostadinova
5. Claudia Klüppelberg

Citations in the corpus

• Ruin Models with Investment Income (2008, methodology): “In [74] a discrete time version of (2.4) is given, while [ 16 , 43, 44, 64, 65] all focus on the asymptotics of ruin probabilities, to be briefly reviewed below.”