Remarks on the Swiss premium principle on positive risks
Abstract In this note it is proved that the Swiss premium principle is completely characterized by its premiums for positive Bernoulli risks. This yields another interpretation of the Swiss premium principle.
On Quasi-Mean Value Principles
Many of the more recently proposed premium calculation principles cannot so far be analyzed on the basis of a unified theory. We introduce a generalized notion of mean value principle, called quasi-mean value principle, which includes the most important principles considered in actuarial science and permits the construction of new ones. This general class contains an attractive subclass of so-called endogeneous quasi-mean value principles. The present work emphasizes properties of this subclass. Our concept has been partly inspired by the expos6 of Muliere and Parmigiani (1993). Properties of premium principles are derived following techniques by Goovaerts et al. (1984). Historically the core of the subject has its origin in the detailed study of mean values by Hardy, Littlewood and Polya (1934). The paper is organized into two parts. In the first part, Section 2, the general definition of the quasi-mean value principle (QMP) is motivated, given, and followed by typical examples matching the new concept. Properties of the QMP are stated in Section 3. The second main part of the paper is devoted to a special endogeneous quasi-mean value principle (EQMP). Its definition is presented in Section 4, also followed by some examples. The topics dealt within the main part are the following ones:
Inhomogeneous Boundary Value Problems for Compressible Navier-Stokes Equations: Well-Posedness and Sensitivity Analysis
In this paper compressible, stationary Navier–Stokes equations are considered. A framework for analysis of such equations is established. In particular, the well-posedness for inhomogeneous boundary value problems of elliptic-hyperbolic type is shown. Analysis is performed for small perturbations of the so-called approximate solutions that take form (1.12). The approximate solutions are determined from Stokes problem (1.11). The small perturbations are given by solutions to (1.13). The uniqueness of solutions for problem (1.13) is proved, and, in addition, the differentiability of solutions with respect to the coefficients of differential operators is shown. The results on the well-posedness of nonlinear problems are interesting on their own and are used to obtain the shape differentiability of the drag functional for incompressible Navier–Stokes equations. The shape gradient of the drag functional is derived in the classical and useful for computations form; an appropriate adjoint state is introduced to ...