Parametric Utility Functions for Decisions Under Uncertainty

This paper was prepared for presentation at the 47th Annual Fall Meeting of the Society of Petroleum Engineers held in San Antonio, Tex., Oct. 8–11, 1972. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by who the paper is presented. Publication elsewhere after publication in the JOURNAL paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract By identifying a few key parameters for certain representative algebraic functions which characterize the decision-maker's economic environment, a meaningful utility function can be defined. The specification of these parameters and the appropriate function describe a unique curve relating utility values to potential monetary values. Parametric utility functions offer Parametric utility functions offer solutions to some perplexing problems where expected value theory does not indicate the best decision. Introduction Application of utility theory has not been well-accepted as a practical procedure in the analysis of investments procedure in the analysis of investments under uncertainty. Although risk economics in the petroleum industry has evolved to the current state of comprehensive probability models, the incorporation of utility methods has been avoided by most model-builders. Economic analysts generally subscribe to the principle of the expected utility calculation, but the difficulties in obtaining a utility function by the traditional utility experiment have made decision-makers reluctant to introduce such curves into routine problem solving. problem solving. The parametric method for obtaining a utility function presents an alternative to the traditional utility experiment. The purpose of the utility experiment is to describe the decision-maker's intrinsic function, but the parametric approach allows the decision-maker to prescribe the transformation that will be used to compute expected utilities. Parametric utility functions can be defined by group deliberation, while the experimental method is basically an individual effort. A parametric utility function can be updated automatically by changing the values of the parameters, without restudying the philosophical basis for the function. A PARTIAL LITERATURE REVIEW The concept of utility was developed by Daniel Bernoulli in his "Exposition of a New Theory on the Measurement of Risk", presented in 1738 to the Imperial Academy of Sciences in Petersburg.