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Optimum portfolio diversification in a general continuous-time model

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  • Aase, Knut Kristian

Abstract

The problem of determining optimal portfolio rules is considered. Prices are allowed to be stochastic processes of a fairly general nature, expressible as stochastic integrals with respect to semimartingales. The set of stochastic differential equations assumed to describe the price behaviour still allows us to handle both the associated control problems and those of statistical inference. The greater generality this approach offers compared to earlier treatments allows for a more realistic fit to real price data. with the obvious implications this has for the applicability of the theory. The additional problem of including consumption is also considered in some generality. The associated Bellman equation has been solved in certain particular situations for illustration. Problems with possible reserve funds, borrowing and shortselling might be handled in the present framework. The problem of statistical inference concerning the parameters in the semimartingale price processes will be treated elsewhere.

Suggested Citation

  • Aase, Knut Kristian, 1984. "Optimum portfolio diversification in a general continuous-time model," Stochastic Processes and their Applications, Elsevier, vol. 18(1), pages 81-98, September.
  • Handle: RePEc:eee:spapps:v:18:y:1984:i:1:p:81-98
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    Citations

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    Cited by:

    1. Ken Sennewald & Klaus Wälde, 2006. "“Itô's Lemma” and the Bellman Equation for Poisson Processes: An Applied View," Journal of Economics, Springer, vol. 89(1), pages 1-36, October.
    2. Jun Liu & Francis A. Longstaff & Jun Pan, 2003. "Dynamic Asset Allocation with Event Risk," Journal of Finance, American Finance Association, vol. 58(1), pages 231-259, February.
    3. Morten Christensen & Eckhard Platen, 2004. "A General Benchmark Model for Stochastic Jump Sizes," Research Paper Series 139, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Sanjiv Ranjan Das & Raman Uppal, 2004. "Systemic Risk and International Portfolio Choice," Journal of Finance, American Finance Association, vol. 59(6), pages 2809-2834, December.
    5. Sennewald, Ken, 2005. "Controlled Stochastic Differential Equations under Poisson Uncertainty and with Unbounded Utility," Dresden Discussion Paper Series in Economics 03/05, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.
    6. repec:spr:joptap:v:161:y:2014:i:1:d:10.1007_s10957-012-0208-1 is not listed on IDEAS
    7. Sennewald, Ken, 2007. "Controlled stochastic differential equations under Poisson uncertainty and with unbounded utility," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1106-1131, April.
    8. Branger, Nicole & Kraft, Holger & Meinerding, Christoph, 2013. "Partial information about contagion risk, self-exciting processes and portfolio optimization," SAFE Working Paper Series 28, Research Center SAFE - Sustainable Architecture for Finance in Europe, Goethe University Frankfurt.
    9. Hatemi-J, Abdulnasser & El-Khatib, Youssef, 2015. "Portfolio selection: An alternative approach," Economics Letters, Elsevier, vol. 135(C), pages 141-143.
    10. Stephan Dieckmann & Michael Gallmeyer, 2006. "Pricing Rare Event Risk in Emerging Markets," 2006 Meeting Papers 305, Society for Economic Dynamics.
    11. Sennewald, Ken & Wälde, Klaus, 2005. ""Itô's Lemma" and the Bellman equation: An applied view," Dresden Discussion Paper Series in Economics 04/05, Technische Universität Dresden, Faculty of Business and Economics, Department of Economics.
    12. Goll, Thomas & Kallsen, Jan, 2000. "Optimal portfolios for logarithmic utility," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 31-48, September.
    13. Marco Piccirilli & Tiziano Vargiolu, 2018. "Optimal Portfolio in Intraday Electricity Markets Modelled by L\'evy-Ornstein-Uhlenbeck Processes," Papers 1807.01979, arXiv.org.
    14. Dieckmann, Stephan & Gallmeyer, Michael, 2005. "The equilibrium allocation of diffusive and jump risks with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 29(9), pages 1547-1576, September.
    15. Castellano, Rosella & Cerqueti, Roy, 2014. "Mean–Variance portfolio selection in presence of infrequently traded stocks," European Journal of Operational Research, Elsevier, vol. 234(2), pages 442-449.
    16. Marcel Prokopczuk, 2011. "Optimal portfolio choice in the presence of domestic systemic risk: empirical evidence from stock markets," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 34(2), pages 141-168, November.
    17. Vedat Akgiray & G. Geoffrey Booth, 1987. "Compound Distribution Models Of Stock Returns: An Empirical Comparison," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 10(3), pages 269-280, September.
    18. Framstad, Nils Chr. & Oksendal, Bernt & Sulem, Agnes, 2001. "Optimal consumption and portfolio in a jump diffusion market with proportional transaction costs," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 233-257, April.
    19. repec:sbe:breart:v:24:y:2004:i:2:a:2711 is not listed on IDEAS
    20. Branger, Nicole & Kraft, Holger & Meinerding, Christoph, 2014. "Partial information about contagion risk, self-exciting processes and portfolio optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 18-36.
    21. Yacine Ait-Sahalia & T. R. Hurd, 2012. "Portfolio Choice in Markets with Contagion," Papers 1210.1598, arXiv.org.
    22. Wee, In-Suk, 1999. "Stability for multidimensional jump-diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 80(2), pages 193-209, April.

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