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
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.