Optimal Consumption of a Generalized Geometric Brownian Motion with Fixed and Variable Intervention Costs
AbstractWe 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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Bibliographic InfoPaper 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.
Length: 25 pages
Date of creation: Jul 2013
Date of revision:
Stochastic Programming; Markov processes; Impulse control; Quasivariational inequalities; Consumption-investment problems with fixed intervention costs;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- D91 - Microeconomics - - Intertemporal Choice - - - Intertemporal Household Choice; Life Cycle Models and Saving
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