A Monte Carlo study of the effect of estimation risk on the optimal solutions of risk programming models

In mathematical risk programming models the decision maker is usually assumed to know the distribution of net returns (when other elements of the planning problem are deterministic). However, this assumption is only justified when the probability distribution of returns represents degrees of belief of the decision maker. When sample data obtained from historical information is used, the existence of estimation error must be recognized. This study at an assesses the importance of estimation error in risk programming through a repeated sampling experiment. Two population distributions were used, a multivariate normal and a combination of independently distributed lognormals. Samples of various sizes (5, 6, 7, 8, 9, 10, 15, 20, 50 and 99 years) were obtained and several risk programming models (QP, MOTAD, Target MOTAD and 5 versions of the Safety-First model) were run 100 times, using the above samples as inputs. The results indicate that the variability of solution vector is very high, particularly at the sample sizes most commonly used in applied work. Although the variance decreases as the sample size gets larger, the solution is still far from convergence, even with 99 years of data. These results hold for normal and non-normal populations as well