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:
Unity Identity Text Self
Abstract Understanding the receptivity of literature, how one work admits many readers, begins with an analogy: unity is to text as identity is to self. Unity here means the way all a text’s features can be related through one central theme. Identity describes a person’s sameness within different behaviors as variations on one identity theme (Lichtenstein). To find unity or identity, however, the interpreter himself plays a behavioral variation on his identity theme. In interpreting, his identity re-creates itself as he shapes the text to match his characteristic defenses, fantasies, and coherences. Thus, what a poet says about fictional, political, or scientific texts expresses the same identity theme as the poems he writes. To understand reading, criticism, and any knowing or making in symbols, then, we need to let go the Cartesian craving for objectivity and accept the themes in ourselves with which we construe the world—including literary works.