A Risk Model with Renewal Shot-Noise Cox Process
Angelos Dassios, Jiwook Jang, Hongbiao Zhao
Insurance: Mathematics and Economics 65 (2015) 55–65
#002267 20160218 ()
In this paper we generalise the risk models beyond the ordinary framework of affine processes or Markov processes and study a risk process where the claim arrivals are driven by a Cox process with renewal shot-noise intensity. The upper bounds of the finite-horizon and infinite-horizon ruin probabilities are investigated and an efficient and exact Monte Carlo simulation algorithm for this new process is developed. A more efficient estimation method for the infinite-horizon ruin probability based on importance sampling via a suitable change of probability measure is also provided; illustrative numerical examples are also provided.
JEL-Codes: G22 C10 C60
Keywords: Risk model Ruin probability Renewal shot-noise Cox process Piecewise-deterministic Markov process Martingale method Importance sampling Change of probability measure Rare-event simulation

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