Skip to main content
SpringerLink
Log in

Mutual Fund Theorem for continuous time markets with random coefficients

  • Published:
Theory and Decision Aims and scope Submit manuscript

Abstract

The optimal investment problem is studied for a continuous time incomplete market model. It is assumed that the risk-free rate, the appreciation rates, and the volatility of the stocks are all random; they are independent from the driving Brownian motion, and they are currently observable. It is shown that some weakened version of Mutual Fund Theorem holds for this market for general class of utilities. It is shown that the supremum of expected utilities can be achieved on a sequence of strategies with a certain distribution of risky assets that does not depend on risk preferences described by different utilities.

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

Access this article

Log in via an institution

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

  • Brennan, M. J. (1998). The role of learning in dynamic portfolio decisions. European Finance Review, 1, 295–306.

    Article  Google Scholar 

  • Dokuchaev, N. (2010a). Mean variance and goal achieving portfolio for discrete-time market with currently observable source of correlations. ESAIM: Control, Optimisation and Calculus of Variations, 16, 635–647.

    Article  Google Scholar 

  • Dokuchaev, N. (2010b). Predictability on finite horizon for processes with exponential decrease of energy on higher frequencies. Signal Processing, 90(2), 696–701.

    Article  Google Scholar 

  • Dokuchaev, N., & Haussmann, U. (2001). Optimal portfolio selection and compression in an incomplete market. Quantitative Finance, 1, 336–345.

    Article  Google Scholar 

  • Feldman, D. (2007). Incomplete information equilibria: Separation theorems and other myths. Annals of Operations Research, 151, 119–149.

    Article  Google Scholar 

  • Karatzas, I., & Shreve, S. E. (1998). Methods of mathematical finance. New York: Springer.

    Book  Google Scholar 

  • Khanna, A., & Kulldorff, M. (1999). A generalization of the mutual fund theorem. Finance and Stochastics, 3, 167–185.

    Article  Google Scholar 

  • Krylov, N. V. (1980). Controlled diffusion processes. New York: Springer.

    Book  Google Scholar 

  • Li, D., & Ng, W. L. (2000). Optimal portfolio selection: Multi-period mean-variance optimization. Mathematical Finance, 10(3), 387–406.

    Article  Google Scholar 

  • Lim, A. (2004). Quadratic hedging and mean-variance portfolio selection with random parameters in an incomplete market. Mathematics of Operations Research, 29(1), 132–161.

    Article  Google Scholar 

  • Lim, A. (2005). Mean-variance hedging when there are jumps. SIAM Journal of Control and Optimization, 44, 1893–1922.

    Article  Google Scholar 

  • Lim, A., & Zhou, X. Y. (2002). Mean-variance portfolio selection with random parameters in a complete market. Mathematics of Operations Research, 27(1), 101–120.

    Article  Google Scholar 

  • Merton, R. (1969). Lifetime portfolio selection under uncertainty: The continuous-time case. Review of Economics and Statistics, 51, 247–257.

    Google Scholar 

  • Revuz, D., & Yor, M. (1999). Continuous martingales and Brownian motion. New York: Springer.

    Book  Google Scholar 

  • Schachermayer, W., Srbu, M., & Taflin, E. (2009). In which financial markets do mutual fund theorems hold true? Finance and Stochastics, 13, 49–77.

    Article  Google Scholar 

  • Shilov, G. E., & Gurevich, B. L. (1967). Integral, measure and derivative: A unified approach. Moscow: Nauka.

    Google Scholar 

Download references

Acknowledgments

This work was supported by ARC Grant of Australia DP120100928 to the author.

Author information

Authors and Affiliations

  1. Department of Mathematics & Statistics, Curtin University, GPO Box U1987, Perth, WA, 6845, Australia

    Nikolai Dokuchaev

Authors
  1. Nikolai Dokuchaev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nikolai Dokuchaev.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dokuchaev, N. Mutual Fund Theorem for continuous time markets with random coefficients. Theory Decis 76, 179–199 (2014). https://doi.org/10.1007/s11238-013-9368-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11238-013-9368-1

Keywords

Search

Navigation