1st International ICST Conference on Performance Evaluation Methodologies and Tools

Research Article

Monte Carlo simulation of killed diffusions with a single barrier

  • @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.