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Stochastic impulse control with discounted and ergodic optimization criteria: A comparative study for the control of risky holdings

Author

Listed:
  • 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

We consider a single-asset investment fund that in the absence of transactions costs would hold a constant amount of wealth in the risky asset. In the presence of market frictions wealth is allowed to fluctuate within a control band: Its upper (lower) boundary is chosen so that gains (losses) from adjustments to the target minus (plus) fixed plus proportional transaction costs maximize (minimize) a power utility function. We compare stochastic impulse control policies derived via ergodic and discounted optimization criteria. For the solution of the ergodic problem we use basic tools from the theory of diffusions whereas the discounted problem is solved after being characterized as a system of quasi-variational inequalities. For both versions of the problem, derivation of the control bands pertains to the numerical solution of a system of nonlinear equations. We solve numerous such systems and present an extensive comparative sensitivity analysis with respect to the parameters that characterize investor’s preferences and market behavior.

Suggested Citation

  • Yiannis Kamarianakis & Anastasios Xepapadeas, 2006. "Stochastic impulse control with discounted and ergodic optimization criteria: A comparative study for the control of risky holdings," Working Papers 0709, University of Crete, Department of Economics.
    • Handle: RePEc:crt:wpaper:0709
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    References listed on IDEAS

    as
    1. Abel Cadenillas & Tahir Choulli & Michael Taksar & Lei Zhang, 2006. "Classical And Impulse Stochastic Control For The Optimization Of The Dividend And Risk Policies Of An Insurance Firm," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 181-202, January.
    2. 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.
    3. Browne, S., 1995. "Optimal Investment Policies for a Firm with a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Papers 95-08, Columbia - Graduate School of Business.
    4. Sid Browne, 1995. "Optimal Investment Policies for a Firm With a Random Risk Process: Exponential Utility and Minimizing the Probability of Ruin," Mathematics of Operations Research, INFORMS, vol. 20(4), pages 937-958, November.
    5. Dumas, Bernard, 1991. "Super contact and related optimality conditions," Journal of Economic Dynamics and Control, Elsevier, vol. 15(4), pages 675-685, October.
    6. Abel Cadenillas & Fernando Zapatero, 2000. "Classical and Impulse Stochastic Control of the Exchange Rate Using Interest Rates and Reserves," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 141-156, April.
    7. J. Michael Harrison & Thomas M. Sellke & Allison J. Taylor, 1983. "Impulse Control of Brownian Motion," Mathematics of Operations Research, INFORMS, vol. 8(3), pages 454-466, August.
    8. 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.
    9. Zakamouline, Valeri I., 2006. "European option pricing and hedging with both fixed and proportional transaction costs," Journal of Economic Dynamics and Control, Elsevier, vol. 30(1), pages 1-25, January.
    10. Yiannis Kamarianakis & Anastasios Xepapadeas, 2006. "Control Bands for Tracking Constant Portfolio Allocations with Fixed and Proportional Transaction Costs," Working Papers 0610, University of Crete, Department of Economics.
    11. 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.
    12. Mundaca, Gabriela & Oksendal, Bernt, 1998. "Optimal stochastic intervention control with application to the exchange rate," Journal of Mathematical Economics, Elsevier, vol. 29(2), pages 225-243, March.
    13. Dixit, Avinash, 1991. "A simplified treatment of the theory of optimal regulation of Brownian motion," Journal of Economic Dynamics and Control, Elsevier, vol. 15(4), pages 657-673, October.
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    More about this item

    Keywords

    Transaction costs; stochastic impulse control; ergodic criteria;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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