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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)

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    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.

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    File URL: http://eco83.econ.unito.it/RePEc/wp/m21.pdf
    File Function: First version, 2013
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    Bibliographic Info

    Paper provided by Department of Economics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino in its series Working papers with number 021.

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    Length: 25 pages
    Date of creation: Jul 2013
    Date of revision:
    Handle: RePEc:tur:wpapnw:021

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    Related research

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

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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. 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. 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.
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