The Exact Solution of Multi-period Portfolio Choice Problem with Exponential Utility

  • Taras Bodnar
  • Nestor ParolyaEmail author
  • Wolfgang Schmid
Conference paper
Part of the Operations Research Proceedings book series (ORP)


In the current paper we derive the exact analytical solution of the multi-period portfolio choice problem for an exponential utility function. It is assumed that the asset returns depend on predictable variables and that the joint random process of the asset returns follows a vector autoregression. We prove that the optimal portfolio weights depend on the covariance matrices of the next two periods and the conditional mean vector of the next period. The case without predictable variables and the case of independent asset returns are partial cases of our solution.


Optimal Portfolio Risky Asset Asset Return Portfolio Weight Absolute Risk Aversion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Bodnar, T., Parolya, N., Schmid, W.: A closed-form solution of the multi-period portfolio choice problem for a quadratic utility function. To appear in Ann. Oper. Res. (2015)Google Scholar
  2. 2.
    Bodnar, T., Parolya, N., Schmid, W.: On the exact solution of the multi-period portfolio choice problem for an exponential utility under return predictability. Accept/minor revision in Eur. J. Oper. Res. (2014). arXiv:1207.1037
  3. 3.
    Bodnar, T., Parolya, N., Schmid, W.: On the equivalence of quadratic optimization problems commonly used in portfolio theory. Eur. J. Oper. Res. 229, 637–644 (2013)CrossRefGoogle Scholar
  4. 4.
    Brandt, M.: Portfolio choice problems. In: Aït-Sahalia, Y., Hansen, L.P. (eds.) Handbook of Financial Econometrics: Tools and Techniques, vol. 1, pp. 269–336. North Holland (2010)Google Scholar
  5. 5.
    Campbell, J.Y., Chan, Y.L., Viceira, L.M.: A multivariate model of strategic asset allocation. J. Financ. Econ. 67, 41–80 (2003)CrossRefGoogle Scholar
  6. 6.
    Çanakoğlu, E., Özekici, S.: Portfolio selection in stochastic markets with exponential utility functions. Ann. Oper. Res. 166, 281–297 (2009)Google Scholar
  7. 7.
    Markowitz, H.: Portfolio selection. J. Finance 7, 77–91 (1952)Google Scholar
  8. 8.
    Merton, R.C.: Lifetime portfolio selection under uncertainty: the continuous time case. Rev. Econ. Stat. 50, 247–257 (1969)CrossRefGoogle Scholar
  9. 9.
    Pennacchi, G.: Theory of Asset Pricing. Pearson/Addison-Wesley, Boston (2008)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.University of StockholmStockholmSweden
  2. 2.Leibniz University HannoverHannoverGermany
  3. 3.European University ViadrinaFrankfurtGermany

Personalised recommendations