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Exponential models by Orlicz spaces and applications

Part of: Linear function spaces and their duals Mathematical finance Sufficiency and information Miscellaneous applications of functional analysis

Published online by Cambridge University Press:  16 November 2018

Marina Santacroce ,
Paola Siri  and
Barbara Trivellato
Marina Santacroce*
Affiliation:
Politecnico di Torino
Paola Siri*
Affiliation:
Politecnico di Torino
Barbara Trivellato*
Affiliation:
Politecnico di Torino
*
* Postal address: Dipartimento di Scienze Matematiche G. L. Lagrange, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
* Postal address: Dipartimento di Scienze Matematiche G. L. Lagrange, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
* Postal address: Dipartimento di Scienze Matematiche G. L. Lagrange, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.
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Abstract

The geometric structure of the nonparametric statistical model of all positive densities connected by an open exponential arc and its intimate relation to Orlicz spaces give new insights to well-known financial objects which arise in exponential utility maximization problems.

Keywords

Orlicz spacemaximal exponential modelexponential utility maximizationminimal entropy martingale measurereverse Hölder condition

MSC classification

Primary: 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46N30: Applications in probability theory and statistics 62B10: Information-theoretic topics 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 3 , September 2018 , pp. 682 - 700
Copyright
Copyright © Applied Probability Trust 2018 

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