Skip to main content
main-content
Top

Hint

Swipe to navigate through the articles of this issue

29-03-2021

Utility maximization in a multidimensional semimartingale model with nonlinear wealth dynamics

Journal:
Mathematics and Financial Economics
Authors:
Mauricio Junca, Rafael Serrano
Important notes

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Abstract

We explore martingale and convex duality techniques to maximize expected risk-averse utility from consumption in a general multi-dimensional (non-Markovian) semimartingale market model with jumps and non-linear wealth dynamics. The model allows to incorporate additional cash flows via non-linear margin payment functions in the drift term that depend on the allocation proportion. These can be used to cast frictions such as the impact of the portfolio choices of a ‘large’ investor on the expected assets’ returns, funding costs arising from differential borrowing and lending rates, and the cash inflow of a firm in a neoclassical economy with constant return-to-scale Cobb–Douglas technology subject to exogenous aggregate shocks. We provide a general verification theorem for random utility fields satisfying the usual Inada conditions, find conditions under which jumps in our model lead to precautionary saving, and present an explicit characterization for CRRA. We report two-fund separation-type results which assert that optimal allocations move along one-dimensional segments, and illustrate our results numerically for various margin payment functions and bounded variation tempered \(\alpha \)-stable jumps.

Please log in to get access to this content

To get access to this content you need the following product:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 58.000 Bücher
  • über 300 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Testen Sie jetzt 30 Tage kostenlos.

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 69.000 Bücher
  • über 500 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Umwelt
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Testen Sie jetzt 30 Tage kostenlos.

Literature
About this article

Premium Partner

    Image Credits