Advertisement

Annals of Finance

, Volume 4, Issue 2, pp 255–268 | Cite as

On the semimartingale property via bounded logarithmic utility

  • Kasper Larsen
  • Gordan Žitković
Research Article

Abstract

This paper provides a new version of the condition of Di Nunno et al. (2003); Di Nunno, G., Meyer-Brandis, T., Øksendal, B., Proske, F.: Optimal portfolio for an insider in a market driven by Levy processes. Quant. Financ. 6, 83–94 (2006). Ankirchner and Imkeller Annales de l’Institut Henri Poincaré (B) Probabilités et statistiques 41, 479–503 (2005) and Biagini and Øksendal Appl. Math. Optim. 52, 167–181 (2005) which ensures the semimartingale property for a large class of continuous stochastic processes. Unlike our predecessors, we base our modeling framework on the concept of portfolio proportions. This yields a short self-contained proof of the main theorem, as well as a counter example which shows that analogues of our results do not hold in the discontinuous setting.

Keywords

Arbitrage Enlargement of filtrations Financial markets Logarithmic utility Semimartingales Stochastic processes Utility maximization 

JEL Classification Numbers

C61 G11 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ankirchner S., Imkeller P. (2005) Finite utility on financial markets with asymmetric information and structure properties of the price dynamics. Annales de l’Institut Henri Poincaré (B) Probabilités et statistiques 41, 479–503CrossRefGoogle Scholar
  2. Björk T., Hult H. (2005) A note on Wick products and the fractional Black-Scholes model. Finance and Stochastics 9, 197–209CrossRefGoogle Scholar
  3. Biagini F., Øksendal B. (2005) A general stochastic calculus approach to insider trading. Appl. Math. Optim. 52, 167–181CrossRefGoogle Scholar
  4. Brémaud P. (1981) Point processes and queues. Springer, Berlin Heidelberg New YorkGoogle Scholar
  5. Delbaen F., Schachermayer W. (1994) A general version of the fundamental theorem of asset pricing. Mathematische Annalen 300, 463–520CrossRefGoogle Scholar
  6. Di Nunno G., Meyer-Brandis T., Øksendal B., Proske F. (2006) Optimal portfolio for an insider in a market driven by Levy processes. Quant. Financ. 6, 83–94CrossRefGoogle Scholar
  7. Karatzas I., Pikovsky I. (1996) Anticipative portfolio optimization. Adv. Appl. Prob. 28, 1095–1122CrossRefGoogle Scholar
  8. Karatzas I., Shreve S.E. (1991) Brownian motion and stochastic calculus, 2nd ed. Springer, Berlin Heidelberg New YorkGoogle Scholar
  9. Protter P.E. (2004) Stochastic integration and differential equations, 2nd ed. Springer, Berlin Heidelberg New YorkGoogle Scholar
  10. Revuz D., Yor M. (1999) Continuous Martingales and Brownian Motion, 3rd ed. Springer, Berlin Heidelberg New YorkGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA
  2. 2.Department of MathematicsUniversity of Texas at AustinAustinUSA

Personalised recommendations