Confronted with high-dimensional data arising from either word-document count, global climate patterns or any one of the myriad other sources, most scientific approaches extract a <i>good</i> low-dimensional summary. This desire to reduce dimensionality may be seen as a consequence of <i>Occam's Razor</i>, and the scientific methodologies we have in mind… (More)
Haezendonck risk measures is a recently introduced class of risk measures which includes, as its minimal member, the Tail Value-at-Risk (T-VaR)-T-VaR arguably the most popular risk measure in global insurance regulation. In applications often one has to estimate the risk measure given a random sample from an unknown distribution. The distribution could… (More)
We show that the empirical mass function associated with a sequence of i.i.d. discrete random variables converges in l r at the (n/log2n) 1/2 rate, for all r ≥ 2. For r < 2 the rate is shown to fail for heavy tailed distributions. The threshold case of r = 2 is explored in detail.
In this thesis we are interested in the impact of economic and financial factors, such as interest rate, tax payment, reinsurance, and investment return, on insurance business. The underlying risk models of insurance business that we consider range from the classical compound Poisson risk model to the newly emerging and more general Lévy risk model. In… (More)
To my parents ii ACKNOWLEDGEMENTS First and foremost, I would like to express my deepest gratitude to my advi-sor, Professor Qihe Tang. I really appreciate that I can be involved in many research projects with Professor Tang in the past four years and hence developed strong interests in exploring different subjects of actuarial science. Without his constant… (More)
Suppose that mn observations are made from the distribution R and n − mn from the distribution S. Associate with each pair, x from R and y from S, a nonnegative score φ(x, y). An optimal reading policy is one that yields a sequence mn that maximizes E(M (n)), the expected sum of the (n − mn)mn observed scores, uniformly in n. The alternating policy, which… (More)