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Optimum portfolio diversification in a general continuous-time model


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  • Aase, Knut Kristian


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.

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Bibliographic Info

Article provided by Elsevier in its journal Stochastic Processes and their Applications.

Volume (Year): 18 (1984)
Issue (Month): 1 (September)
Pages: 81-98

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Handle: RePEc:eee:spapps:v:18:y:1984:i:1:p:81-98

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Keywords: portfolio selection stochastic control martingales stochastic integrals;


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Cited by:
  1. 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.
  2. Sennewald, Ken, 2005. "Controlled Stochastic Differential Equations under Poisson Uncertainty and with Unbounded Utility," Dresden Discussion Paper Series in Economics 03/05, Dresden University of Technology, Faculty of Business and Economics, Department of Economics.
  3. 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.
  4. Goll, Thomas & Kallsen, Jan, 2000. "Optimal portfolios for logarithmic utility," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 31-48, September.
  5. 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.
  6. Marcel Prokopczuk, 2011. "Optimal portfolio choice in the presence of domestic systemic risk: empirical evidence from stock markets," Decisions in Economics and Finance, Springer, vol. 34(2), pages 141-168, November.
  7. 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.
  8. Sennewald, Ken & Wälde, Klaus, 2005. ""Itô's Lemma" and the Bellman equation: An applied view," Dresden Discussion Paper Series in Economics 04/05, Dresden University of Technology, Faculty of Business and Economics, Department of Economics.
  9. Sennewald, Ken & Wälde, Klaus, 2005. ""Ito's Lemma" and the Bellman equation for Poisson processes: An applied view," W.E.P. - Würzburg Economic Papers 58, University of Würzburg, Chair for Monetary Policy and International Economics.
  10. 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.
  11. 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.
  12. Stephan Dieckmann & Michael Gallmeyer, 2006. "Pricing Rare Event Risk in Emerging Markets," 2006 Meeting Papers 305, Society for Economic Dynamics.
  13. Liu, Jun & Longstaff, Francis & Pan, Jun, 2001. "Dynamic Asset Allocation with Event Risk," University of California at Los Angeles, Anderson Graduate School of Management qt9fm6t5nb, Anderson Graduate School of Management, UCLA.
  14. 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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