2 results
21 - Determining a Unique Q
- from Part V - Applications in Financial Economics
-
- Book:
- Point Processes and Jump Diffusions
- Published online:
- 27 May 2021
- Print publication:
- 17 June 2021, pp 227-239
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- Chapter
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Orlicz Addition for Measures and an Optimization Problem for the
$f$-divergence
- Part of
-
- Journal:
- Canadian Journal of Mathematics / Volume 72 / Issue 2 / April 2020
- Published online by Cambridge University Press:
- 16 July 2019, pp. 455-479
- Print publication:
- April 2020
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- Article
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This paper provides a functional analogue of the recently initiated dual Orlicz–Brunn–Minkowski theory for star bodies. We first propose the Orlicz addition of measures, and establish the dual functional Orlicz–Brunn–Minkowski inequality. Based on a family of linear Orlicz additions of two measures, we provide an interpretation for the famous
$f$-divergence. Jensen’s inequality for integrals is also proved to be equivalent to the newly established dual functional Orlicz–Brunn–Minkowski inequality. An optimization problem for the 
$f$-divergence is proposed, and related functional affine isoperimetric inequalities are established.
