Divergent and convergent margins in the north-western Alps - Confrontation to actualistic models

Divergent and convergent margins actualistic models are reviewed and applied to the history of the western Alps. Tethyan rifting history and geometry are analyzed: the northern European margin is considered as an upper plate whereas the southern Apulian margin is a lower plate; the Breche basin is regarded as the former break-away trough; the internal Brianconnais domain represents the northern rift shoulder whilst the more external domains are regarded as the infill of a complex rim basin locally affected by important extension (Valaisan and Vocontain trough). The Schistes lustres and ophiolites of the Tsate nappe are compared to an accretionary prism: the imbrication of this nappe elements is regarded as a direct consequence of the accretionary phenomena already active in early Cretaceous; the Gets/Simme complex could orginate from a more internal part of the accretionary prism. Some eclogitic basements represent the former Apulian margin substratum (Sesia) others (Mont-Rose) are interpreted as the former edge of the European margin. The history of the closing Tethyan domain is analyzed and the remaining problems concerning the cinematics, the presence/absence of a volcanic arc and the eoalpine metamorphism are discussed.

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.