This course introduces the theory of compound Poisson processes, with a particular emphasis on their application to insurance portfolios (though their applicability in other areas is also noted)

Topics include: Modelling loss distributions; Skewed parametric distribution families; Method of moments, method of percentiles and maximum likelihood estimation; Pearson goodness-of-fit testing for distribution assessment; Truncated and censored data, including applications to reinsurance and policy excess schemes; Random sums, convolutions and compound distributions, particularly for modeling aggregate claim distributions; Normal and gamma approximations to compound distributions; Compound Poisson process theory, including applications to insurance portfolio surplus processes; Ultimate and finite-time ruin probabilities; Adjustment coefficients and optimal reinsurance contracts.

To achieve an understanding of and facility in applying and communicating the following topics:

• Estimating using skewed distributions with and without the presence of censoring and truncation
• Aggregation of random quantities through compound distribution theory
• Compound Poisson process theory including approximation of boundary crossing probabilities as applied to calculating risk for insurance portfolios

• Assignment 20%
• Final Exam 80%

Three contact hours per week plus private study time.

STAT3004 Stochastic Modelling

Please refer to Course Website