Markov Chain Monte Carlo for Risk Measures

Yuya Suzuki, Thorbjörn Gudmundsson

2014

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.

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