A Cox process with log-normal intensity

In this paper we look at pricing stop-loss reinsurance contracts using an approximation technique similar to that of Basu (Ph.D. Thesis, London, 1999) and Rogers and Shi [Journal of Applied Probability 32 (4) (1995) 1077–1088] for processes with constant claims and the underlying stochastic intensity following a log-normal distribution. In particular, we look at the Cox process with the underlying stochastic intensity being log-normal.