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Optimal Consumption of a Generalized Geometric Brownian Motion with Fixed and Variable Intervention Costs

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  • Stefano Baccarin

    () (Department of Economics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino, Italy)

Abstract

We consider the problem of maximizing expected lifetime utility from consumption of a generalized geometric Brownian motion in the presence of controlling costs with a fixed component. Under general assumptions on the utility function and the intervention costs our main result is to show that, if the discount rate is large enough, there always exists an optimal impulse policy for this problem, which is of a Markovian type. We compute explicitly the optimal consumption in the case of constant coefficients of the process, linear utility and a two values discount rate. In this illustrative example the value function is not C1 and the verification theorems commonly used to characterize the optimal control cannot be applied.

Suggested Citation

  • Stefano Baccarin, 2013. "Optimal Consumption of a Generalized Geometric Brownian Motion with Fixed and Variable Intervention Costs," Working papers 021, Department of Economics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino.
  • Handle: RePEc:tur:wpapnw:021
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    File URL: http://www.biblioecon.unito.it/biblioservizi/RePEc/tur/wpapnw/m21.pdf
    File Function: First version, 2013
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    References listed on IDEAS

    as
    1. Vathana Ly Vath & Mohamed Mnif & Huyên Pham, 2007. "A model of optimal portfolio selection under liquidity risk and price impact," Finance and Stochastics, Springer, vol. 11(1), pages 51-90, January.
    2. Bar-Ilan, Avner & Perry, David & Stadje, Wolfgang, 2004. "A generalized impulse control model of cash management," Journal of Economic Dynamics and Control, Elsevier, vol. 28(6), pages 1013-1033, March.
    3. Alessandra Cretarola & Fausto Gozzi & Huyên Pham & Peter Tankov, 2011. "Optimal consumption policies in illiquid markets," Finance and Stochastics, Springer, vol. 15(1), pages 85-115, January.
    4. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
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    More about this item

    Keywords

    Stochastic Programming; Markov processes; Impulse control; Quasivariational inequalities; Consumption-investment problems with fixed intervention costs;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making

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