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Mathematics and Financial Economics
Published in: Mathematics and Financial Economics 4/2015

01-10-2015

Non-concave utility maximisation on the positive real axis in discrete time

Authors: Laurence Carassus, Miklós Rásonyi, Andrea M. Rodrigues

Published in: Mathematics and Financial Economics | Issue 4/2015

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Abstract

We treat a discrete-time asset allocation problem in an arbitrage-free, generically incomplete financial market, where the investor has a possibly non-concave utility function and wealth is restricted to remain non-negative. Under easily verifiable conditions, we establish the existence of optimal portfolios.
previous article Envelope theorems in Banach lattices and asset pricing

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Appendix
Available only for authorised users
Footnotes
1
Here \(x^{+}\triangleq \max \left\{ x,0\right\} \) and \(x^{-}\triangleq -\min \left\{ x,0\right\} \) for every \(x\in \mathbb {R}\). Furthermore, in order to make the notation less heavy, given any function \(f:~X\rightarrow \mathbb {R}\), we shall write henceforth \(f^{\pm }\left( x\right) \triangleq \left[ f\left( x\right) \right] ^{\pm }\) for all \(x\in X\).
 
2
To be precise, in the cited lemma there is strict inequality in (2.5) and it is required to hold for \(\lambda >1\) only. As easily seen, it works also for our version.
 
3
Given a set \(E\subseteq X\times Y\), we recall that the projection of \(E\) on \(X\) is
$$\begin{aligned} {\text {Proj}}_{X}\!\left( E\right) \triangleq \left\{ x\in X\text {: }\exists \,y\in Y\text { such that }\left( x,y\right) \in E\right\} . \end{aligned}$$
 
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Metadata
Title
Non-concave utility maximisation on the positive real axis in discrete time
Authors
Laurence Carassus
Miklós Rásonyi
Andrea M. Rodrigues
Publication date
01-10-2015
Publisher
Springer Berlin Heidelberg
Published in
Mathematics and Financial Economics / Issue 4/2015
Print ISSN: 1862-9679
Electronic ISSN: 1862-9660
DOI
https://doi.org/10.1007/s11579-015-0146-4