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The ␣-level value at risk (VaR) and the ␣-level conditional tail expectation (CTE) of a continuous random variable X are defined as its ␣-level quantile (denoted by q ␣) and its conditional expectation given the event {X Ͼ q ␣ }, respectively. VaR is a popular risk measure in the banking sector, for both external and internal reporting purposes, while the… (More)

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)

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.

The ␣-level Conditional Tail Expectation (CTE) of a continuous random variable X is defined as its conditional expectation given the event {X Ͼ q ␣ }, where q ␣ represents its ␣-level quantile. It is well known that the empirical CTE (the average of the n(1 Ϫ ␣) largest order statistics in a sample of size n) is a negatively biased estimator of the CTE.… (More)

- Fan Yang, Palle Jorgensen, J. Tyler Leverty, Nariankadu D. Shyamalkumar, Ting Zhang, Weimin Han +12 others
- 2016

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)

Should a seller use a multi-unit auction for identical and indivisible units of a good? We show, under specific assumptions on the value distributions of the bidders, that in large markets the multi-unit format generates higher (lower) expected revenue compared to the bundled format when the supply is relatively scarce (abundant). In contrast, a large… (More)

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