# 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