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

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

No 21, Working papers from Department of Economics, Social Studies, Applied Mathematics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino

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.

Keywords: Stochastic Programming, Markov processes, Impulse control, Quasivariational inequalities; Consumption-investment problems with fixed intervention costs (search for similar items in EconPapers)
JEL-codes: C61 D91 (search for similar items in EconPapers)
Pages: 25 pages
Date: 2013-07
New Economics Papers: this item is included in nep-ore
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