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The bi-atomic uniform minimal solution of Schmitter's problem

โœ Scribed by F. De Vylder; M. Goovaerts; E. Marceau

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
664 KB
Volume
20
Category
Article
ISSN
0167-6687

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โœฆ Synopsis

The problem posed by Schmitter was to maximize the ruin probability when mean and variance of the claim size distribution are given. In this note we prove that the minimal ruin probability is given by the bi-atomic distribution with the maximal possible claim size as one of its mass points. A by-product is a lower bound c e -pu for the ruin probability ~(u), where p is the adjustment coefficient, and c a constant not depending on the allowed claim size distributions.

๐Ÿ“œ SIMILAR VOLUMES

The solution of Schmitter's simple probl
The solution of Schmitter's simple problem: Numerical illustration
โœ F. De Vylder; M. Goovaerts; E. Marceau ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 826 KB

Numerical illustrations are given of the technique to solve Schmitter's problem proposed in De Vylder and Marceau (1996).

On the Minimal Solution of the Problem o
On the Minimal Solution of the Problem of Primitives
โœ Benedetto Bongiorno ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 82 KB

We characterize the primitives of the minimal extension of the Lebesgue integral which also integrates the derivatives of differentiable functions (called the Cintegral). Then we prove that each BV function is a multiplier for the C-integral and that the product of a derivative and a BV function is

Minimal regularity of the solution of so
Minimal regularity of the solution of some boundary value problems of Signorini's type in polygonal domains
โœ Denis Mercier; Serge Nicaise ๐Ÿ“‚ Article ๐Ÿ“… 2005 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 152 KB

## Abstract We study the regularity in Sobolev spaces of the solution of transmission problems in a polygonal domain of the plane, with unilateral boundary conditions of Signorini's type in a part of the boundary and Dirichlet or Neumann boundary conditions on the remainder part. We use a penalizat