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Decision Making Based on a Nonparametric Shape-Preserving Perturbation of a Reference Utility Function

Jian Hu(jianhu***at***umich.edu)

Abstract: This paper develops a robust optimization based decision-making framework using a nonparametric perturbation of a reference utility function. The perturbation preserves the risk-aversion property but solves the problem of ambiguity and inconsistency in eliciting the reference utility function. We study the topology of the perturbation, and show that in the decision-making framework the price of perturbation is increasing and concave. When the reference utility is given at discrete points, we reformulate this optimization problem as a second-order cone program. The Monte Carlo sampling method is used to solve the general case that a reference utility is a continuous function, and the convergence of this method is proved. The usefulness of the robust utility optimization framework is illustrated with the help of a portfolio investment decision problem.

Keywords: Expected Utility Maximization, Robust Optimization, Nonparametric Perturbation, Sensitivity Analysis, Portfolio Optimization

Category 1: Robust Optimization

Category 2: Stochastic Programming

Category 3: Applications -- OR and Management Sciences (Finance and Economics )


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Entry Submitted: 11/25/2013
Entry Accepted: 11/25/2013
Entry Last Modified: 11/25/2013

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