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Controlling the risky fraction process with an ergodic criterion

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  • Yiannis Kamarianakis

    ()
    (Regional Analysis Division, Institute of Applied and Computational Mathematics, Foundation for Research and Technology-Hellas, Greece)

  • Anastasios Xepapadeas

    ()
    (Department of Economics, University of Crete, Greece)

Abstract

This article examines a tracking problem, similar to the one presented in Pliska and Suzuki (Quantitative Finance, 2004): an investor would keep constant proportions of her wealth in different assets if markets were frictionless; however, in the presence of fixed and proportional transaction costs her implementation problem is to keep asset proportions close to the target levels whilst avoiding too much intervention costs. Instead of minimizing discounted tracking error plus transaction costs over an infinite horizon, the optimization objective here is minimization of long run tracking error plus intervention costs per unit time. This ergodic problem is treated via combining basic tools from diffusion theory and nonlinear optimization techniques. A comparative sensitivity analysis of the ergodic and discounted problems is undertaken.

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Bibliographic Info

Paper provided by University of Crete, Department of Economics in its series Working Papers with number 0710.

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Length: 21 pages
Date of creation: 10 Oct 2006
Date of revision:
Handle: RePEc:crt:wpaper:0710

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  1. R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
  2. Cadenillas, Abel & Zapatero, Fernando, 1999. "Optimal Central Bank Intervention in the Foreign Exchange Market," Journal of Economic Theory, Elsevier, vol. 87(1), pages 218-242, July.
  3. Luis Alvarez & Jukka Virtanen, 2006. "A class of solvable stochastic dividend optimization problems: on the general impact of flexibility on valuation," Economic Theory, Springer, vol. 28(2), pages 373-398, 06.
  4. L.C.G. Rogers, 2001. "The relaxed investor and parameter uncertainty," Finance and Stochastics, Springer, vol. 5(2), pages 131-154.
  5. Dorsey, Robert E & Mayer, Walter J, 1995. "Genetic Algorithms for Estimation Problems with Multiple Optima, Nondifferentiability, and Other Irregular Features," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 53-66, January.
  6. Jose M. Plehn-Dujowich, 2005. "The Optimality of a Control Band Policy," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(4), pages 877-901, October.
  7. Sid Browne, 2000. "Risk-Constrained Dynamic Active Portfolio Management," Management Science, INFORMS, vol. 46(9), pages 1188-1199, September.
  8. Ralf Korn, 1999. "Some applications of impulse control in mathematical finance," Computational Statistics, Springer, vol. 50(3), pages 493-518, December.
  9. Yuming Li, 1993. "Growth-Security Investment Strategy for Long and Short Runs," Management Science, INFORMS, vol. 39(8), pages 915-924, August.
  10. Stanley Pliska & Kiyoshi Suzuki, 2004. "Optimal tracking for asset allocation with fixed and proportional transaction costs," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 233-243.
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