Gaggero, Mauro and Gnecco, Giorgio and Sanguineti, Marcello Suboptimal Policies for Stochastic NStage Optimization Problems: Accuracy Analysis and a Case Study from Optimal Consumption. In: Models and Methods in Economics and Management. International Series in Operations Research & Management Science (198). Springer, pp. 2750. ISBN 9783319006697 (2014)
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Abstract
Dynamic Programming formally solves stochastic optimization problems with an objective that is additive over a finite number of stages. However, it provides closedform solutions only in particular cases. In general, one has to resort to approximate methodologies. In this chapter, suboptimal solutions are searched for by approximating the decision policies via linear combinations of Gaussian and sigmoidal functions containing adjustable parameters, to be optimized together with the coefficients of the combinations. These approximation schemes correspond to Gaussian radialbasisfunction networks and sigmoidal feedforward neural networks, respectively. The accuracies of the suboptimal solutions are investigated by estimating the error propagation through the stages. As a case study, we address a multidimensional problem of optimal consumption under uncertainty, modeled as a stochastic optimization task with an objective that is additive over a finite number of stages. In the classical onedimensional context, a consumer aims at maximizing over a given time horizon the discounted expected value of consumption of a good, where the expectation is taken with respect to a stochastic interest rate. The consumer has an initial wealth and at each time period earns an income, modeled as an exogenous input. We consider a multidimensional framework, in which there are d>1 consumers that aim at maximizing a social utility function. First we provide conditions that allow one to apply our estimates to such a problem; then we present a numerical analysis.
Item Type:  Book Section 

Identification Number:  10.1007/9783319006697_3 
Additional Information:  Essays in Honor of Charles S. Tapiero 
Subjects:  Q Science > QA Mathematics > QA75 Electronic computers. Computer science 
Research Area:  Computer Science and Applications 
Depositing User:  Giorgio Gnecco 
Date Deposited:  17 Sep 2013 13:00 
Last Modified:  18 Feb 2015 11:45 
URI:  http://eprints.imtlucca.it/id/eprint/1784 
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Suboptimal policies for stochastic Nstage optimization problems: accuracy analysis and a case study from optimal consumption. (deposited 12 Sep 2013 12:20)
 Suboptimal Policies for Stochastic NStage Optimization Problems: Accuracy Analysis and a Case Study from Optimal Consumption. (deposited 17 Sep 2013 13:00) [Currently Displayed]
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