Sublinear functionals and conical measures

2001 ◽  
Vol 77 (1) ◽  
pp. 56-64 ◽  
Author(s):  
H. König
Keyword(s):  
Sublinear Functionals

scholarly journals Banach limits, infinite matrices and sublinear functionals

1969 ◽  
Vol 26 (3) ◽  
pp. 640-655 ◽  
Author(s):  
S Simons
Keyword(s):  
Infinite Matrices ◽  
Banach Limits ◽  
Sublinear Functionals

Geometric bounds on certain sublinear functionals of geometric Brownian motion

2003 ◽  
Vol 40 (4) ◽  
pp. 893-905 ◽  
Author(s):  
Per Hörfelt
Keyword(s):  
Distribution Function ◽  
Brownian Motion ◽  
Borel Measure ◽  
Random Variable ◽  
Geometric Brownian Motion ◽  
Upper And Lower Bounds ◽  
Tail Probabilities ◽  
Absolutely Continuous ◽  
Basket Options ◽  
Sublinear Functionals

Suppose that {Xs, 0 ≤ s ≤ T} is an m-dimensional geometric Brownian motion with drift, μ is a bounded positive Borel measure on [0,T], and ϕ : ℝm → [0,∞) is a (weighted) lq(ℝm)-norm, 1 ≤ q ≤ ∞. The purpose of this paper is to study the distribution and the moments of the random variable Y given by the Lp(μ)-norm, 1 ≤ p ≤ ∞, of the function s ↦ ϕ(Xs), 0 ≤ s ≤ T. By using various geometric inequalities in Wiener space, this paper gives upper and lower bounds for the distribution function of Y and proves that the distribution function is log-concave and absolutely continuous on every open subset of the distribution's support. Moreover, the paper derives tail probabilities, presents sharp moment inequalities, and shows that Y is indetermined by its moments. The paper will also discuss the so-called moment-matching method for the pricing of Asian-styled basket options.

Some properties of spaces of sublinear functionals

1977 ◽  
Vol 18 (2) ◽  
pp. 308-317 ◽  
Author(s):  
A. A. Tolstonogov
Keyword(s):  
Sublinear Functionals

On a property of extended sublinear functionals

1977 ◽  
Vol 8 (3) ◽  
pp. 339-341
Author(s):  
Jacques Bair
Keyword(s):  
Sublinear Functionals

Noncoercive variational inequalities with application to friction problems

1991 ◽  
Vol 117 (3-4) ◽  
pp. 275-293 ◽  
Author(s):  
P. Shi ◽  
M. Shillor
Keyword(s):  
Variational Inequalities ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Obstacle Problems ◽  
Elastic Contact ◽  
Compatibility Conditions ◽  
Sublinear Functionals ◽  
Noncoercive Variational Inequalities ◽  
Necessary And Sufficient

SynopsisNoncoercive variational inequalities with sublinear functionals are considered. Necessary and sufficient conditions are given for the solvability of such problems. These conditions are in the form of compatibility conditions-for the data, as well as the boundedness of the solutions to related problems. These results are used for the obstacle problems for the membrance and the elastic contact in the presence of friction.

scholarly journals Sublinear functionals and Knopp's core theorem

1990 ◽  
Vol 13 (3) ◽  
pp. 461-468 ◽  
Author(s):  
C. Orhan
Keyword(s):  
Sublinear Functionals ◽  
Bounded Sequences

In this paper we are concerned with inequalities involving certain sublinear functionals onm, the space of real bounded sequences. Such inequalities being analogues of Knopp's Core theorem.

scholarly journals Minimal sublinear functionals

1970 ◽  
Vol 37 (1) ◽  
pp. 37-56 ◽  
Author(s):  
S. Simons
Keyword(s):  
Sublinear Functionals

Sublinear functionals defined on a cone

1970 ◽  
Vol 11 (2) ◽  
pp. 327-336 ◽  
Author(s):  
A. M. Rubinov
Keyword(s):  
Sublinear Functionals

Disintegration of dominated monotone sublinear functionals on the space of measurable functions

1993 ◽  
Vol 34 (6) ◽  
pp. 1117-1134
Author(s):  
A. A. Lebedev
Keyword(s):  
Measurable Functions ◽  
Sublinear Functionals

scholarly journals Nonlinear expectations of random sets

2020 ◽  
Vol 25 (1) ◽  
pp. 5-41
Author(s):  
Ilya Molchanov ◽  
Anja Mühlemann
Keyword(s):  
Random Sets ◽  
Linear Spaces ◽  
Infinite Dimensional ◽  
Closed Sets ◽  
Construction Methods ◽  
Dual Representations ◽  
Random Closed Sets ◽  
Sublinear Functionals ◽  
Primal And Dual ◽  
Nonlinear Expectations

AbstractSublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued functions (which form a nonlinear space) or, equivalently, on random closed sets. This calls for a separate study of sublinear and superlinear expectations, since a change of sign does not alter the direction of the inclusion in the set-valued setting.We identify the extremal expectations as those arising from the primal and dual representations of nonlinear expectations. Several general construction methods for nonlinear expectations are presented and the corresponding duality representation results are obtained. On the application side, sublinear expectations are naturally related to depth trimming of multivariate samples, while superlinear ones can be used to assess utilities of multiasset portfolios.

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