Optimizing agricultural land-use portfolios with scarce data-A non-stochastic model

The theory of portfolio selection has often been applied to help improve economic decisions about the environment. Applying this theory requires information on the covariance of uncertain returns between all combinations of the economic options and also assumes that returns are normally distributed. As it is usually difficult to fulfill all data requirements and assumptions, this paper proposes a variant of robust portfolio optimization as an alternative that needs less pre-information. The approach considers future uncertainties in a non-stochastic fashion through possible deviations from the nominal return of land-use alternatives. Maximizing the economic return of the land-use portfolio is conditional on meeting an inclusive set of constraints. These demand that a pre-defined return threshold is achieved by the robust solution for each uncertainty scenario considered. Based on data for eight agricultural crops common in the Ecuadorian lowlands, a comparison with portfolios generated by classical stochastic mean-variance optimization shows greater land-use diversification (through increased Shannon indices), but only moderate expected economic loss of non-stochastic robust land-use portfolios. We conclude that non-stochastic derivation of land-use portfolios is a good alternative to the classical stochastic model, in situations where information on economic input parameters is scarce.