Importance Sampling for a Simple Markovian Intensity Model Using Subsolutions

Boualem Djehiche, Henrik Hult, Pierre Nyquist

Research output: Contribution to journalArticlepeer-review


This article considers importance sampling for estimation of rare-event probabilities in a specific collection of Markovian jump processes used for, e.g., modeling of credit risk. Previous attempts at designing importance sampling algorithms have resulted in poor performance and the main contribution of the article is the design of efficient importance sampling algorithms using subsolutions. The dynamics of the jump processes cause the corresponding Hamilton-Jacobi equations to have an intricate state-dependence, which makes the design of efficient algorithms difficult. We provide theoretical results that quantify the performance of importance sampling algorithms in general and construct asymptotically optimal algorithms for some examples. The computational gain compared to standard Monte Carlo is illustrated by numerical examples.

Original languageEnglish (US)
Article number14
JournalACM Transactions on Modeling and Computer Simulation
Issue number2
StatePublished - Apr 2022


  • Credit risk
  • Importance sampling
  • Large deviations
  • Markovian intensity models
  • Monte Carlo

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computer Science Applications


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