scholarly journals A Stop Loss Inequality for Compound Poisson Processes with a Unimodal Claimsize Distribution

1977 ◽  
Vol 9 (1-2) ◽  
pp. 247-256 ◽  
Author(s):  
H. G. Verbeek
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Compound Poisson Process ◽  
Compound Poisson ◽  
Jump Size ◽  
Specific Assumption ◽  
Stop Loss ◽  
Size Variable ◽  
Insight Into ◽  
Underlying Risk

The paper considers the problem of finding an upper bound for the Stop loss premium.We will start with a brief sketch of the practical context in which this problem is relevant.If it is reasonable to assume, that the accumulated claims variable of the underlying risk can be represented by a Compound Poisson Process, the following data are needed for fixing the Stop loss premium:— the claims intensity,— the distribution of the claimsizes (jump-size variable).In practical situations it is usually possible to find a reasonable estimate for the claims intensity (expected number of claims in a given period).Generally speaking, however, it is not so easy to get sufficient data on the claimsize distribution. Ordinarily only its mean is known. This deficiency in information can of course be offset by assuming the unknown distribution to be one of the familiar types, such as Exponential, Gamma or Pareto.Stop loss premiums are however very sensitive to variations in the type of claimsize distribution and consequently it can make a lot of difference in the result what particular choice is made.To gain some insight into the consequences of a specific assumption, it is useful to know within what range the premium can move for varying distributional suppositions. This means establishing an upper bound and a lower bound. The lower bound is trivially obtained if the mass of the claimsize distribution is solely concentrated at its mean. The upper bound on the other hand should correspond to the “worst” possible claimsize distribution. This means, that we have to look for a distribution which maximizes the Stop loss premium.

scholarly journals Estimation of the Jump Size Density in a Mixed Compound Poisson Process

2015 ◽  
Vol 42 (4) ◽  
pp. 1023-1044 ◽  
Author(s):  
Fabienne Comte ◽  
Celine Duval ◽  
Valentine Genon-Catalot ◽  
Johanna Kappus
Keyword(s):  
Poisson Process ◽  
Compound Poisson Process ◽  
Compound Poisson ◽  
Jump Size ◽  
Mixed Compound

scholarly journals Induced Matchings and the v-Number of Graded Ideals

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2860
Author(s):  
Gonzalo Grisalde ◽  
Enrique Reyes ◽  
Rafael H. Villarreal
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Matching Number ◽  
Edge Ideal ◽  
Induced Matching ◽  
Simplicial Partition ◽  
The Family ◽  
Induced Matchings ◽  
Edge Ring ◽  
Insight Into

We give a formula for the v-number of a graded ideal that can be used to compute this number. Then, we show that for the edge ideal I(G) of a graph G, the induced matching number of G is an upper bound for the v-number of I(G) when G is very well-covered, or G has a simplicial partition, or G is well-covered connected and contains neither four, nor five cycles. In all these cases, the v-number of I(G) is a lower bound for the regularity of the edge ring of G. We classify when the induced matching number of G is an upper bound for the v-number of I(G) when G is a cycle and classify when all vertices of a graph are shedding vertices to gain insight into the family of W2-graphs.

scholarly journals On the Numerical Evaluation of Stop-Loss Premiums

1979 ◽  
Vol 10 (3) ◽  
pp. 318-324 ◽  
Author(s):  
F. Covens ◽  
M. Van Wouwe ◽  
M. Goovaerts
Keyword(s):  
Poisson Process ◽  
Numerical Evaluation ◽  
Fourier Transforms ◽  
Numerical Procedure ◽  
Compound Poisson Process ◽  
Risk Process ◽  
Compound Poisson ◽  
Stop Loss

A numerical procedure is described to evaluate the stop-loss premium in case the risk process is a compound Poisson process. The method is mainly based on an algorithm of R. Piessens and M. Branders for the numerical evaluation of Fourier transforms.

Approximation of sums by compound Poisson distributions with respect to stop-loss distances

1990 ◽  
Vol 22 (2) ◽  
pp. 350-374 ◽  
Author(s):  
S. T. Rachev ◽  
L. Rüschendorf
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Compound Poisson ◽  
Poisson Distributions ◽  
Stop Loss ◽  
Scale Transformations

The approximation of sums of independent random variables by compound Poisson distributions with respect to stop-loss distances is investigated. These distances are motivated by risk-theoretic considerations. In contrast to the usual construction of approximating compound Poisson distributions, the method suggested in this paper is to fit several moments. For two moments, this can be achieved by scale transformations. It is shown that the new approximations are more stable and improve the usual approximations by accompanying laws in examples where the probability 1 – pi that the ith summand is zero is not too large.

scholarly journals Multiple closed orbits for N-body-type problems

1998 ◽  
Vol 58 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Shiqing Zhang
Keyword(s):  
Lower Bound ◽  
Periodic Solutions ◽  
Upper Bound ◽  
Critical Value ◽  
Body Type ◽  
Fixed Energy ◽  
Closed Orbits

Using the equivariant Ljusternik-Schnirelmann theory and the estimate of the upper bound of the critical value and lower bound for the collision solutions, we obtain some new results in the large concerning multiple geometrically distinct periodic solutions of fixed energy for a class of planar N-body type problems.

Limit Cycle Bifurcations for Piecewise Smooth Hamiltonian Systems with a Generalized Eye-Figure Loop

2016 ◽  
Vol 26 (12) ◽  
pp. 1650204 ◽  
Author(s):  
Jihua Yang ◽  
Liqin Zhao
Keyword(s):  
Lower Bound ◽  
Limit Cycle ◽  
Hamiltonian Systems ◽  
Limit Cycles ◽  
Upper Bound ◽  
Melnikov Function ◽  
Piecewise Smooth ◽  
First Order ◽  
Period Annulus

This paper deals with the limit cycle bifurcations for piecewise smooth Hamiltonian systems. By using the first order Melnikov function of piecewise near-Hamiltonian systems given in [Liu & Han, 2010], we give a lower bound and an upper bound of the number of limit cycles that bifurcate from the period annulus between the center and the generalized eye-figure loop up to the first order of Melnikov function.

Isolated minima of the product of n linear forms

1953 ◽  
Vol 49 (1) ◽  
pp. 59-62 ◽  
Author(s):  
E. S. Barnes
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Linear Forms ◽  
Image Position

Letbe n linear forms with real coefficients and determinant Δ = ∥ aij∥ ≠ 0; and denote by M(X) the lower bound of | X1X2 … Xn| over all integer sets (u) ≠ (0). It is well known that γn, the upper bound of M(X)/|Δ| over all sets of forms Xi, is finite, and the value of γn has been determined when n = 2 and n = 3.

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