Monte Carlo simulation of killed diffusions with a single barrier

Bruno  Casella; Gareth O.  Roberts

1st International ICST Conference on Performance Evaluation Methodologies and Tools

Research Article

Monte Carlo simulation of killed diffusions with a single barrier

Cite: BibTeX Plain Text

@INPROCEEDINGS{10.1145/1190095.1190151,
    author={Bruno  Casella and Gareth O.  Roberts},
    title={Monte Carlo simulation of killed diffusions with a single barrier},
    proceedings={1st International ICST Conference on Performance Evaluation Methodologies and Tools},
    publisher={ACM},
    proceedings_a={VALUETOOLS},
    year={2012},
    month={4},
    keywords={Exact Algorithm crossing probability Rao-Blackwellization Brownian bridge.},
    doi={10.1145/1190095.1190151}
}

Bruno Casella
Gareth O. Roberts
Year: 2012
Monte Carlo simulation of killed diffusions with a single barrier
VALUETOOLS
ACM
DOI: 10.1145/1190095.1190151

Bruno Casella¹^,*, Gareth O. Roberts¹^,*

1: Department of Mathematics and Statistics, Lancaster University, Bailrigg, Lancaster, UK, LA1 4YW

*Contact email: b.casella@lancaster.ac.uk, g.o.roberts@lancaster.ac.uk

Abstract

We present a simple algorithm for Monte Carlo simulation of killed diffusions with a single barrier. The algorithm returns an unbiased, Rao-Blackwellized Monte Carlo estimator for a certain class diffusion processes. Notably, the explicit knowledge of the transition laws of the process is not a prerequisite for our unbiased Monte Carlo method. The numerical test demonstrates that the proposed estimator performs very favorably in comparison to competitors based on discretization schemes.

Keywords: Exact Algorithm crossing probability Rao-Blackwellization Brownian bridge.

Published: 2012-04-12
Publisher: ACM

: http://dx.doi.org/10.1145/1190095.1190151