Skip to main content
Log in

On the semimartingale property via bounded logarithmic utility

  • Research Article
  • Published:
Annals of Finance Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • 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, 479–503

    Article  Google Scholar 

  • Björk T., Hult H. (2005) A note on Wick products and the fractional Black-Scholes model. Finance and Stochastics 9, 197–209

    Article  Google Scholar 

  • Biagini F., Øksendal B. (2005) A general stochastic calculus approach to insider trading. Appl. Math. Optim. 52, 167–181

    Article  Google Scholar 

  • Brémaud P. (1981) Point processes and queues. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Delbaen F., Schachermayer W. (1994) A general version of the fundamental theorem of asset pricing. Mathematische Annalen 300, 463–520

    Article  Google Scholar 

  • 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, 83–94

    Article  Google Scholar 

  • Karatzas I., Pikovsky I. (1996) Anticipative portfolio optimization. Adv. Appl. Prob. 28, 1095–1122

    Article  Google Scholar 

  • Karatzas I., Shreve S.E. (1991) Brownian motion and stochastic calculus, 2nd ed. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Protter P.E. (2004) Stochastic integration and differential equations, 2nd ed. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Revuz D., Yor M. (1999) Continuous Martingales and Brownian Motion, 3rd ed. Springer, Berlin Heidelberg New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gordan Žitković.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Larsen, K., Žitković, G. On the semimartingale property via bounded logarithmic utility. Annals of Finance 4, 255–268 (2008). https://doi.org/10.1007/s10436-006-0067-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10436-006-0067-6

Keywords

JEL Classification Numbers

Navigation