Nonlinear expectations of random sets

被引:0
|
作者
Ilya Molchanov
Anja Mühlemann
机构
[1] University of Bern,Institute of Mathematical Statistics and Actuarial Science
来源
Finance and Stochastics | 2021年 / 25卷
关键词
Multiasset portfolio; Random set; Selection expectation; Sublinear expectation; Superlinear expectation; Set-valued function; Transaction costs; Utility; 28B20; 49J53; 60D05; 62H99; 91B16; C18; C65;
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摘要
Sublinear 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.
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页码:5 / 41
页数:36
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