Markov Chain Monte Carlo for Risk Measures

Yuya Suzuki, Thorbjörn Gudmundsson

Abstract

In this paper, we consider random sums with heavy-tailed increments. By the term random sum, we mean a sum of random variables where the number of summands is also random. Our interest is to construct an efficient method to calculate tail-based risk measures such as quantiles and conditional expectation (expected shortfalls). When assuming extreme quantiles and heavy-tailed increments, using standard Monte Carlo method can be inefficient. In previous works, there exists an efficient method to sample rare-events (tail-events) using a Markov chain Monte Carlo (MCMC) with a given threshold. We apply the sampling method to estimate statistics based on tail-information, with a given rare-event probability. The performance is compared with other methods by some numerical results in the case increments follow Pareto distributions. We also show numerical results with Weibull, and Log-Normal distributions. Our proposed method is shown to be efficient especially in cases of extreme tails.

References

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Paper Citation


in Harvard Style

Suzuki Y. and Gudmundsson T. (2014). Markov Chain Monte Carlo for Risk Measures . In Proceedings of the 4th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH, ISBN 978-989-758-038-3, pages 330-338. DOI: 10.5220/0005035303300338


in Bibtex Style

@conference{simultech14,
author={Yuya Suzuki and Thorbjörn Gudmundsson},
title={Markov Chain Monte Carlo for Risk Measures},
booktitle={Proceedings of the 4th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},
year={2014},
pages={330-338},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005035303300338},
isbn={978-989-758-038-3},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 4th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,
TI - Markov Chain Monte Carlo for Risk Measures
SN - 978-989-758-038-3
AU - Suzuki Y.
AU - Gudmundsson T.
PY - 2014
SP - 330
EP - 338
DO - 10.5220/0005035303300338