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Authors: Yuya Suzuki 1 and Thorbjörn Gudmundsson 2

Affiliations: 1 KTH Royal Institute of Technology and Keio University, Sweden ; 2 Royal Institute of Technology, Sweden

ISBN: 978-989-758-038-3

Keyword(s): Markov Chain Monte Carlo, Risk Measures,Heavy Tails, Rare-event Simulation.

Related Ontology Subjects/Areas/Topics: Complex Systems Modeling and Simulation ; Computer Simulation Techniques ; Crisis Modeling and Simulation ; Formal Methods ; Mathematical Simulation ; Risk Analysis ; Simulation and Modeling ; Simulation Tools and Platforms ; Stochastic Modeling and Simulation

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.

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Paper citation in several formats:
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

@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},
}

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

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