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We study multiline insurance companies with limited liability and limited capital, creating the possibility of insurer default. Insurance premiums are determined by no-arbitrage option pricing methods. The results are developed under the realistic assumption that the losses created by insurer default are allocated among policyholders following an ex post, pro rata, sharing rule. In general, the ratio of default costs to expected claims, and thus the ratios of premiums to expected claims vary across insurance lines. Moreover, capital and related costs are allocated across lines in proportion to each line’s share of a digital default option on the insurer. Our results differ from those derived elsewhere in the literature.

In this article, the hydrodynamic behavior of dilute aqueous solutions of a natural polysaccharide—gellan in the porous media under the modeled oilfield conditions is described. The hydrodynamic properties of gellan and poly(acrylamide) solutions in saline porous media are compared. The influence of inorganic salts NaCl, KCl, CaCl2, MgCl2, and BaСl2 on sol–gel and gel–sol transitions of dilute gellan solutions was evaluated. The mechanism of sol–gel transition in the presence of individual alkaline and alkaline-earth metal salts is described on the basis of literature data. The viscometric measurements revealed that the effectiveness of salts to enhance gelation of gellan changes in the following order: BaСl2 > CaCl2 ≈ MgCl2 > KCl > NaCl. The sol–gel and gel–sol phase transitions of gellan solution were also observed upon addition of oil field water containing 73 g L−1 of alkaline and alkaline earth metal ions. During the injection of gellan solutions into the porous media saturated by saline water an oscillation of the injection pressure was observed. Such behavior of gellan is explained by either the sol-to-gel and the gel-to-sol transitions of the polymer taking place in saline water or the step-by-step plugging of high permeable channels until all high permeable channels of sand packs are plugged due to gellan invasion. The application of brine-initiated gelation of gellan for water shutoff operations (WSO) in field conditions was demonstrated. Higher technological effectiveness of gellan injection in comparison with existing gelation systems was shown. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015, 132, 41256.

In this paper we prove the analogues of Khintchine, Marcinkiewicz-Zygmund and Rosenthal moment inequalities for symmetric statistics of second order in not identically distributed random variables.