Displaying similar documents to “Optimal domains for kernel operators on [0,∞) × [0,∞)”

Optimal domains for the kernel operator associated with Sobolev's inequality

Guillermo P. Curbera, Werner J. Ricker (2003)

Studia Mathematica

Similarity:

Refinements of the classical Sobolev inequality lead to optimal domain problems in a natural way. This is made precise in recent work of Edmunds, Kerman and Pick; the fundamental technique is to prove that the (generalized) Sobolev inequality is equivalent to the boundedness of an associated kernel operator on [0,1]. We make a detailed study of both the optimal domain, providing various characterizations of it, and of properties of the kernel operator when it is extended to act in its...

Optimal Sobolev imbedding spaces

Ron Kerman, Luboš Pick (2009)

Studia Mathematica

Similarity:

This paper continues our study of Sobolev-type imbedding inequalities involving rearrangement-invariant Banach function norms. In it we characterize when the norms considered are optimal. Explicit expressions are given for the optimal partners corresponding to a given domain or range norm.

On the optimal reinsurance problem

Swen Kiesel, Ludger Rüschendorf (2013)

Applicationes Mathematicae

Similarity:

In this paper we consider the optimal reinsurance problem in endogenous form with respect to general convex risk measures ϱ and pricing rules π. By means of a subdifferential formula for compositions in Banach spaces we first characterize optimal reinsurance contracts in the case of one insurance taker and one insurer. In the second step we generalize the characterization to the case of several insurance takers. As a consequence we obtain a result saying that cooperation brings less...

On optimal matching measures for matching problems related to the Euclidean distance

José Manuel Mazón, Julio Daniel Rossi, Julián Toledo (2014)

Mathematica Bohemica

Similarity:

We deal with an optimal matching problem, that is, we want to transport two measures to a given place (the target set) where they will match, minimizing the total transport cost that in our case is given by the sum of two different multiples of the Euclidean distance that each measure is transported. We show that such a problem has a solution with an optimal matching measure supported in the target set. This result can be proved by an approximation procedure using a p -Laplacian system....

Discrete time optimal dividend problem with constant premium and exponentially distributed claims

Dariusz Socha (2014)

Applicationes Mathematicae

Similarity:

An optimal dividend problem is studied consisting in maximisation of expected discounted dividend payments until ruin time. A solution of this problem for constant premium d and exponentially distributed claims is presented. It is shown that an optimal policy is a barrier policy. Moreover, an analytic way to solve this problem is sketched.

Optimal streams of premiums in multiperiod credibility models

L. Gajek, P. Miś, J. Słowińska (2007)

Applicationes Mathematicae

Similarity:

Optimal arrangement of a stream of insurance premiums for a multiperiod insurance policy is considered. In order to satisfy solvency requirements we assume that a weak Axiom of Solvency is satisfied. Then two optimization problems are solved: finding a stream of net premiums that approximates optimally 1) future claims, or 2) "anticipating premiums". It is shown that the resulting optimal streams of premiums enable differentiating between policyholders much more quickly than one-period...