Generalized Poisson random variables: Their distributional properties and actuarial applications

Estimating the expected number of claims per risk exposure period is essential to risk classification. The simple Poisson regression model usually cannot fit the claim data well because the data often display over-dispersion. Various other models, such as Negative binomial distribution and Poisson-Inverse Gaussian distribution, have been proposed to address the issue of over-dispersion. Additionally, zero-inflated count distributions, such as the zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB), have been proposed to account for a larger number of observed zeros in insurance loss data. The Generalized Poisson (GP) distribution, introduced in 1973, can model over-dispersed and under-dispersed data and has been found in applications in many areas, including actuarial science. The principal purpose of this thesis is to study in detail the application of GP and its related distributions in modeling insurance claim numbers. In Chapter 2, we study the distributional properties of a family of distributions that includes GP as a special case. We first derive recursive formulas for computing the corresponding compound distributions; then, we show that the compound distribution can be evaluated based on the transformation methods such as Fast Fourier Transform (FFT). The results are used to compute risk measures, e.g., Value-at-risk (VaR) and conditional tail expected value (CTE) of the compound distribution. In Chapter 3, we show that the ZI/hurdle + functional form of the GP model can fit insurance loss data well. In addition, we discuss approaches for incorporating exposure into zero-inflated models. In Chapter 4, we introduce a Sarmonov-type bivariate version of the GP distribution. We discuss their zero-inflated and hurdle versions and use them to fit bivariate insurance claim data

Modeling and forecasting of international tourism demand in ASEAN countries

This study attempts to find the best model to forecast international tourism demand using a series of key macroeconomic variables in ASEAN countries. Generally, we find that generalized Poisson regression model is the best one for estimating long-run international tourism demand. In addition, we find that inflation and real exchange rate have negative relationship with international tourism demand. On the other hand, foreign direct investment and openness of trade have positive relationship with international tourism demand. Cointegration test result shows that there is a long-run relationship between variables