A direct approach to the discounted penalty function

This paper provides a new and accessible approach to establishing certain results concerning the discounted penalty function. The direct approach consists of two steps. In the first step, closed-form expressions are obtained in the special case in which the claim amount distribution is a combination of exponential distributions. A rational function is useful in this context. For the second step, one observes that the family of combinations of exponential distributions is dense. Hence, it suffices to reformulate the results of the first step to obtain general results. The surplus process has downward and upward jumps, modeled by two independent compound Poisson processes. If the distribution of the upward jumps is exponential, a series of new results can be obtained with ease. Subsequently, certain results of Gerber and Shiu [H. U. Gerber and E. S. W. Shiu, North American Actuarial Journal 2(1): 48–78 (1998)] can be reproduced. The two-step approach is also applied when an independent Wiener process is added to the surplus process. Certain results are related to Zhang et al. [Z. Zhang, H. Yang, and S. Li, Journal of Computational and Applied Mathematics 233: 1773–1 784 (2010)], which uses different methods.

The TREAT-NMD DMD Global Database: Analysis of More than 7,000 Duchenne Muscular Dystrophy Mutations.

Analyzing the type and frequency of patient-specific mutations that give rise to Duchenne muscular dystrophy (DMD) is an invaluable tool for diagnostics, basic scientific research, trial planning, and improved clinical care. Locus-specific databases allow for the collection, organization, storage, and analysis of genetic variants of disease. Here, we describe the development and analysis of the TREAT-NMD DMD Global database (http://umd.be/TREAT_DMD/). We analyzed genetic data for 7,149 DMD mutations held within the database. A total of 5,682 large mutations were observed (80% of total mutations), of which 4,894 (86%) were deletions (1 exon or larger) and 784 (14%) were duplications (1 exon or larger). There were 1,445 small mutations (smaller than 1 exon, 20% of all mutations), of which 358 (25%) were small deletions and 132 (9%) small insertions and 199 (14%) affected the splice sites. Point mutations totalled 756 (52% of small mutations) with 726 (50%) nonsense mutations and 30 (2%) missense mutations. Finally, 22 (0.3%) mid-intronic mutations were observed. In addition, mutations were identified within the database that would potentially benefit from novel genetic therapies for DMD including stop codon read-through therapies (10% of total mutations) and exon skipping therapy (80% of deletions and 55% of total mutations).