Abstract
This research develops and expands the concept of risk-premium to a multivariate environment, providing an operational framework for the analysis of mean-variance optimizers’ attitudes towards exogenous uncertainty. Firstly, it digresses over possible approximations to the risk premium. Secondly, importance and properties of the variance of the objective function are highlighted. Thirdly, impact of uncertainty on the objective function and on control variables of mean-variance agents is confronted with that of expected function optimizer’s. The analysis is also applied to ex-post flexible or adjustable environments with respect to the decision variables. Production theory examples are briefly sketched. Innovation in tools include matrix algebra results and representation of higher than second moments – with reference to the multinormal as a special case -, and implicit rules of first-order condition point-wise optimization of functions of expected value and of variance of other functions.
Keywords. Multivariate Uncertainty, Multivariate Risks, Risk-Premium and Risk-aversion, Background Noise, Firm’s Valuation, Mean-Variance, Commitment under Uncertainty.
JEL. D80; D21. L14; L15. G11; G12. C60, C61, C69. C10.
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