scholarly journals The Esscher Premium Principle: A Criticism

1981 ◽  
Vol 12 (1) ◽  
pp. 77-78 ◽  
Author(s):  
Benjamin Zehnwirth
Keyword(s):  
Loss Function ◽  
Utility Theory ◽  
Random Quantity ◽  
Present Note ◽  
Random Variable ◽  
Point Of View ◽  
The Other ◽  
Important Distinction ◽  
Image Position ◽  
Insight Into

The Esscher premium principle has recently had some exposure, namely, with the works of Bühlmann (1980) and Gerber (1980).Bühlmann (1980) devised the principle and coined the name for it within the framework of utility theory and risk exchange. Geruber (1980), on the other hand, gives further insight into the principle by studying it within the realm of forecasting in much the same spirit as credibility theorists forecast premiums. However, there is an important distinction: the choice of loss function.The present note sets out to criticize this relatively embryonic principle using decision theoretic arguments and indicates that the Esscher premium is essentially a small perturbation of the well established linearized credibility premium Bühlmann (1970).Let H denote the Esscher premium principle with loading h > o. That is, if X is an observable random variable and Y is a parameter (a risk or a random quantity) to be forecasted then the Esscher premium is given byThat is, H(Y ∣ X) is the Bayes decision rule for estimating Y given the data X relative to the loss functionwhere a is the estimate of Y, and of course the loading h is greater than zero.Now, for the clincher. This loss function is nonsensical from the point of view of estimation. It indicates a loss (or error) to the forecaster that is essentially the antithesis of relative loss.

scholarly journals Some Remarks on a Recent Paper by Borch

1961 ◽  
Vol 1 (5) ◽  
pp. 265-272 ◽  
Author(s):  
Paul Markham Kahn
Keyword(s):  
Distribution Function ◽  
Random Variable ◽  
Fixed Number ◽  
Point Of View ◽  
Optimum Amount ◽  
Measurable Transformation ◽  
The Difference ◽  
Image Position ◽  
Stop Loss ◽  
Condition B

In his recent paper, “An Attempt to Determine the Optimum Amount of Stop Loss Reinsurance”, presented to the XVIth International Congress of Actuaries, Dr. Karl Borch considers the problem of minimizing the variance of the total claims borne by the ceding insurer. Adopting this variance as a measure of risk, he considers as the most efficient reinsurance scheme that one which serves to minimize this variance. If x represents the amount of total claims with distribution function F (x), he considers a reinsurance scheme as a transformation of F (x). Attacking his problem from a different point of view, we restate and prove it for a set of transformations apparently wider than that which he allows.The process of reinsurance substitutes for the amount of total claims x a transformed value Tx as the liability of the ceding insurer, and hence a reinsurance scheme may be described by the associated transformation T of the random variable x representing the amount of total claims, rather than by a transformation of its distribution as discussed by Borch. Let us define an admissible transformation as a Lebesgue-measurable transformation T such thatwhere c is a fixed number between o and m = E (x). Condition (a) implies that the insurer will never bear an amount greater than the actual total claims. In condition (b), c represents the reinsurance premium, assumed fixed, and is equal to the expected value of the difference between the total amount of claims x and the total retained amount of claims Tx borne by the insurer.

A System of Linear Equations with an Infinity of Unknowns

1924 ◽  
Vol 22 (3) ◽  
pp. 282-286
Author(s):  
E. C. Titchmarsh
Keyword(s):  
Present Note ◽  
Linear Equations ◽  
The Other ◽  
System Of Linear Equations ◽  
Other Hand ◽  
Image Position ◽  
Monotonic Character

I have collected in the present note some theorems regarding the solution of a certain system of linear equations with an infinity of unknowns. The general form of the equations isthe numbers a1, a2, … c1, c2, … being given. Equations of this type are of course well known; but in studying them it is generally assumed that the series depend for convergence on the convergence-exponent of the sequences involved, e.g. that and are convergent. No assumptions of this kind are made here, and in fact the series need not be absolutely convergent. On the other hand rather special assumptions are made with regard to the monotonic character of the sequences an and cn.

scholarly journals REPRESENTING CONJUNCTIVE DEDUCTIONS BY DISJUNCTIVE DEDUCTIONS

2016 ◽  
Vol 10 (1) ◽  
pp. 145-157
Author(s):  
KOSTA DOŠEN ◽  
ZORAN PETRIĆ
Keyword(s):  
Point Of View ◽  
The Other ◽  
Theoretical Point ◽  
Single Object ◽  
Finite Products ◽  
Image Position ◽  
Propositional Letter

AbstractA skeleton of the category with finite coproducts${\cal D}$ freely generated by a single object has a subcategory isomorphic to a skeleton of the category with finite products ${\cal C}$ freely generated by a countable set of objects. As a consequence, we obtain that ${\cal D}$ has a subcategory equivalent with ${\cal C}$. From a proof-theoretical point of view, this means that up to some identifications of formulae the deductions of pure conjunctive logic with a countable set of propositional letters can be represented by deductions in pure disjunctive logic with just one propositional letter. By taking opposite categories, one can replace coproduct by product, i.e., disjunction by conjunction, and the other way round, to obtain the dual results.

On the Polygons Inscribed in one Conic and Circumscribed to Another

1924 ◽  
Vol 22 (2) ◽  
pp. 163-166
Author(s):  
W. Burnside
Keyword(s):  
Difference Equation ◽  
Present Note ◽  
Elliptic Functions ◽  
Point Of View ◽  
Image Position

This problem is in general treated in connection with the division of the periods of the elliptic functions. It is the object of the present note to shew, from a purely algebraical point of view, that the condition of closing of the polygon depends solely on a difference equation of the form

Psychological and Ontological Aspects of Causality According to the Philosophy of Sāṃkhya and the Philosophy of Gilles Deleuze

2018 ◽  
Vol 12 (1) ◽  
pp. 104-125
Author(s):  
Julija Bonai
Keyword(s):  
Causal Relationship ◽  
Potential Field ◽  
Ethical Theory ◽  
Gilles Deleuze ◽  
Point Of View ◽  
The Other ◽  
Close Reading ◽  
Human Psyche ◽  
Mode Of Being ◽  
Insight Into

Sāṃkhya, or the philosophy of Yoga, is considered to be one of the most influential traditional philosophies in India. A close reading of it can lead to the conclusion that Sāṃkhya's and Deleuze's philosophy share similar ontological assumptions, especially regarding the material field of immanence that manifests itself through every mode of being. Both philosophies assume modes or degrees of material coexistence that extend from the virtual, potential field of immanence, as something conditional and causal, to actual manifestation that is more or less structured, graspable and shaped. Additionally, they both consider the human psyche to be material that, as materiality itself, manifests itself through different modes of (un)conscious existence. On the other hand, they also share the assumption about the transcendental field of impersonal consciousness immersed in the material field of immanence. This paper identifies and explains the causal relationship among these different modes of being from the point of view of a particular understanding of time, and offers insight into how the comprehension of causality could be implied in ethical theory.

The Social Meaning of Leisure in the Modern World

1950 ◽  
Vol 12 (4) ◽  
pp. 411-421 ◽  
Author(s):  
Josef Pieper
Keyword(s):  
Social Problem ◽  
Point Of View ◽  
The Other ◽  
Modern World ◽  
Social Meaning ◽  
Field Of Vision ◽  
The Social ◽  
The World ◽  
Philosophical Consideration ◽  
Insight Into

My intention is: to try to face a certain central social problem in its connection with the concept of leisure. And I hope that a solution of that problem, or at least some ways towards a solution, may become more clear and visible. This is a rather modest purpose (because problems are still not solved when a solution has become visible or even when some ways of a solution have become more clear than before).I shall not consider the social problem from a formally sociological point of view or from a formally political point of view, but from a philosophical point of view. It shall not be spoken of in such a way that the field of vision is completely filled with it. The point-of-view does not lie so close to the concrete phenomena that our attention is occupied and consumed by their immediate impact. Philosophical consideration means that a certain subject is considered within the horizon of the total and universal reality; it belongs to the essence and nature of a really philosophical question, that not only this question itself comes into play, but that—onsidering, meditating this question—one is obliged to bring into play the totality of the world, even God and the world. In such a view the discussion loses perhaps some actual interest for the politician or for an immediately-involved man. But on the other hand, it might be that deeper possibilities of a solution become perceivable, just because the totality of the real world, especially the totality of human nature, comes into the range of vision. It might be, too, that there are social and political problems which, from the mere viewpoint of sociology and politics, cannot be solved. And perhaps this possibility is relevant to our present case. I would like to formulate the claim very modestly. In question is a sort of attempt, a proposal, to view the problem from a new and familiar standpoint. There may result an insight into the social problem—which possibly can become useful within the sphere of politics.

scholarly journals On Some Divisibility Properties of

1964 ◽  
Vol 7 (4) ◽  
pp. 513-518 ◽  
Author(s):  
P. Erdös
Keyword(s):  
Simple Proof ◽  
Present Note ◽  
The Other ◽  
Other Hand ◽  
Image Position ◽  
Divisibility Properties

L. Moser [3] recently gave a very simple proof that1.has no solutions. In the present note we shall first of all prove that for , which by the fact that there is a prime p satisfying n < p ≤ 2n immediately implies that2.has no solutions. It is easy to see on the other hand that3.has infinitely many non-trivial solutions.

Some Admissible Estimators in Extreme Value Densities

1975 ◽  
Vol 18 (1) ◽  
pp. 105-110
Author(s):  
R. Singh
Keyword(s):  
Real Number ◽  
Loss Function ◽  
Measurable Function ◽  
Random Variable ◽  
Extreme Value ◽  
Lebesgue Measurable Function ◽  
Single Observation ◽  
Squared Error ◽  
Parametric Functions ◽  
Image Position

Let X be a random variable having the extreme value density of the form(1)where r is assumed to be a positive Lebesgue measurable function of x and the function q is defined byfor all θ in Ω = (0, ∞). It is further assumed that q(θ) approaches zero as θ → ∞.In this note we are concerned with estimating parametric functions g(θ) of the form [1/q(θ)]α, α any real number. The loss function is assumed to be squared error and the estimators are assumed to be functions of a single observation X.

scholarly journals On a class of measures of dispersion with application to optimal reinsurance

1969 ◽  
Vol 5 (2) ◽  
pp. 249-266 ◽  
Author(s):  
Jan Ohlin
Keyword(s):  
Random Variable ◽  
Optimal Choice ◽  
Expected Value ◽  
The Other ◽  
Total Risk ◽  
Central Value ◽  
Measures Of Dispersion ◽  
Image Position ◽  
Reinsurance Treaty ◽  
Random Fluctuations

In this paper we will investigate the following reinsurance problem: An insurer, whose total claims for a certain period may be regarded as a random variable x with expected value Ex = m, wishes to cede part of his business to a reinsurer. A reinsurance treaty will consist of rule for the division of x between the two parties. For any observed value of x it should define uniquely what amount should be borne by the ceding insurer. The amount borne by the reinsurer is then simply the remaining part of x.We shall assume that the insurer has already decided how much of his business he wishes to cede, in the sense that he wants to retain a part of the total risk with expected value m — c, where c is a fixed constant, o < c < m.Using the terminology introduced by Kahn in (2) we will describe a reinsurance contract by a transformation (or function) T that for a given x yields the amount Tx borne by the cedent. The random variable x is thus divided into two partsand the properties of the reinsurance contract described by T are summarized in the distributions of the two random variables Tx and (1 — T)x = — Tx.The motivation for reinsurance is generally held to be a desire for stability, in other words the cedent wishes to choose a T such that the random fluctuations in Tx are in some sense smaller than those of x. This choice will in our case be performed under the restriction that ETx = m — c.It is clear that we can never talk about an optimal choice of T without defining exactly what criterion we shall use when comparing two transformations, T1 and T2. According to the above, the criterion should refer to the properties of the distributions of T1x and T2x, so that if one distribution is “more concentrated” around some central value, the corresponding transformation is deemed preferable to the other. However, we still have to define what we mean by “more concentrated”.

Can the Academic Self-Concept be Positive and Realistic?

2005 ◽  
Vol 19 (3) ◽  
pp. 129-132 ◽  
Author(s):  
Reimer Kornmann
Keyword(s):  
Academic Performance ◽  
Opposite Effect ◽  
Self Esteem ◽  
Point Of View ◽  
The Other ◽  
Self Concept ◽  
High Ability ◽  
Self Image ◽  
Other Hand

Summary: My comment is basically restricted to the situation in which less-able students find themselves and refers only to literature in German. From this point of view I am basically able to confirm Marsh's results. It must, however, be said that with less-able pupils the opposite effect can be found: Levels of self-esteem in these pupils are raised, at least temporarily, by separate instruction, academic performance however drops; combined instruction, on the other hand, leads to improved academic performance, while levels of self-esteem drop. Apparently, the positive self-image of less-able pupils who receive separate instruction does not bring about the potential enhancement of academic performance one might expect from high-ability pupils receiving separate instruction. To resolve the dilemma, it is proposed that individual progress in learning be accentuated, and that comparisons with others be dispensed with. This fosters a self-image that can in equal measure be realistic and optimistic.

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