scholarly journals Premium Calculation by Transforming the Layer Premium Density

1996 ◽  
Vol 26 (1) ◽  
pp. 71-92 ◽  
Author(s):  
Shaun Wang
Keyword(s):  
Distribution Function ◽  
Decision Theory ◽  
Stochastic Dominance ◽  
Measure Theory ◽  
Additive Measure ◽  
Proportional Hazard ◽  
Economic Decision ◽  
Recent Developments ◽  
Premium Calculation ◽  
Economic Decision Theory

AbstractThis paper examines a class of premium functionals which are (i) comonotonic additive and (ii) stochastic dominance preservative. The representation for this class is a transformation of the decumulative distribution function. It has close connections with the recent developments in economic decision theory and non-additive measure theory. Among a few elementary members of this class, the proportional hazard transform seems to stand out as being most plausible for actuaries.

Optimal Inspection Methodology for Offshore Structures Based on an Economic Decision Theory

2004 ◽  
Author(s):  
Saul Florentino ◽  
David De Leon ◽  
Jorge Silva
Keyword(s):  
Decision Theory ◽  
Structural Integrity ◽  
Offshore Structures ◽  
Mathematical Framework ◽  
Economic Decision ◽  
Structural Deterioration ◽  
Safety Margins ◽  
Deterioration Process ◽  
Maintenance And Inspection ◽  
Economic Decision Theory

About 200 marine platforms are installed in the Mexican sector of the Gulf of Mexico so that maintenance and inspection schedules play an important role to avoid excessive structural deterioration of the oil facilities and at the same time to keep the facilities within acceptable safety margins. Large costs associated with inspection and repair actions moved managers towards the application of an optimal strategy in order to minimize inspection expenses. For these purposes, it is necessary to consider deterioration process such as fatigue crack growth under the influence of uncertain wave loading which is the dominant force while effort is focused on maintaining structural integrity and safe production. This paper presents an optimal inspection methodology for offshore structures based on an economic decision theory, bearing in mind that large costs are associated with structural failure and extensive inspection and repairs. A system failure analysis of a given sub set of the critical structural components is included as well as a mathematical framework for the assessment of failure and repair cost associated.

Multiple Decision Theory: Recent Developments.

1983 ◽  
Vol 78 (383) ◽  
pp. 732
Author(s):  
P. K. Sen ◽  
Shanti S. Gupta ◽  
Deng-Yuan Huang
Keyword(s):  
Decision Theory ◽  
Recent Developments

scholarly journals Set-Operational Properties of Semiatoms in Non-additive Measure Theory

2001 ◽  
Vol 263 (2) ◽  
pp. 637-654 ◽  
Author(s):  
Toshiaki Murofushi ◽  
Katsushige Fujimoto
Keyword(s):  
Measure Theory ◽  
Additive Measure

scholarly journals On Characterization of Distortion Premium Principle

2003 ◽  
Vol 33 (01) ◽  
pp. 1-10 ◽  
Author(s):  
Xianyi Wu ◽  
Jinglong Wang
Keyword(s):  
Distribution Function ◽  
Integral Representation ◽  
Necessary Condition ◽  
Additive Measure ◽  
Insurance Risk ◽  
Sufficient And Necessary Condition

In this paper, based on the additive measure integral representation of a non-additive measure integral, it is shown that any comonotonically additive premium principle can be represented as an integral of the distorted decumulative distribution function of the insurance risk. Furthermore, a sufficient and necessary condition that a premium principle is a distortion premium principle is given.

scholarly journals Неограниченные сходимости в конвергентных векторных решетках

2018 ◽  
Author(s):  
Y.A.M. Dabboorasad ◽  
E.Yu. Emelyanov
Keyword(s):  
Risk Measures ◽  
Measure Theory ◽  
Variational Calculus ◽  
Mathematical Finance ◽  
Norm Convergence ◽  
Order Convergence ◽  
Vector Lattices ◽  
Almost Everywhere ◽  
Recent Developments ◽  
Compactness Arguments

Various convergences in vector lattices were historically a subject of deep investigation which stems from the begining of the 20th century in works of Riesz, Kantorovich, Nakano, Vulikh, Zanen, and many other mathematicians. The study of the unbounded order convergence had been initiated by Nakano in late 40th in connection with Birkhoff's ergodic theorem. The idea of Nakano was to define the almost everywhere convergence in terms of lattice operations without the direct use of measure theory. Many years later it was recognised that the unbounded order convergence is also rathe useful in probability theory. Since then, the idea of investigating of convergences by using their unbounded versions, have been exploited in several papers. For instance, unbounded convergences in vector lattices have attracted attention of many researchers in order to find new approaches to various problems of functional analysis, operator theory, variational calculus, theory of risk measures in mathematical finance, stochastic processes, etc. Some of those unbounded convergences, like unbounded norm convergence, unbounded multi-norm convergence, unbounded $\tau$-convergence are topological. Others are not topological in general, for example: the unbounded order convergence, the unbounded relative uniform convergence, various unbounded convergences in lattice-normed lattices, etc. Topological convergences are, as usual, more flexible for an investigation due to the compactness arguments, etc. The non-topological convergences are more complicated in genelal, as it can be seen on an example of the a.e-convergence. In the present paper we present recent developments in convergence vector lattices with emphasis on related unbounded convergences. Special attention is paid to the case of convergence in lattice multi pseudo normed vector lattices that generalizes most of cases which were discussed in the literature in the last 5 years.

Sign in / Sign up

Export Citation Format

Share Document