By T. Goodall
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Additional resources for Adequate Decision Rules for Portfolio Choice Problems
Keeping in mind that problems of prediction are inherent in problems of decision under Knightian risk, combining the two parameters into one decision rule is thus more than plausible. 39 chapter three A N A LY S I S O F P R O M I N E N T DECISION RULES A D E Q U AT E D E C I S I O N R U L E S F O R PORTFOLIO CHOICE PROBLEMS But it is plausible only if the investment is repeated an inﬁnite number of times, since underneath Markowitz’s decision rule lies the expected value of the random variable (R – E[R])2.
Expected utility analysis has established two major lines of research. 7 Its inﬂuence was such that for a long time a decision rule could only be declared ‘rational’ by its proponents, if it complied with the expected utility’s axioms. The other line of research treated the expected utility principle as descriptive, and exposed it to empirical analysis. Serving both normative and descriptive analysis has undoubtedly contributed to its predominant role. On the other hand, its serving two masters has caused the expected utility principle to become a prime example of the continuing blurring of normative and descriptive decision theory.
The second approach has since Roy (1952) been called the ‘safety ﬁrst approach’. Safety ﬁrst rules emphasise those results of a gamble that might or should be considered ‘disastrous’ by the individual. Decision rules are considered ‘reasonable and probable in practice’,4 if they lead to a reduction as far as possible of the chances of a catastrophic occurrence. Thus, instead of relying on parameters alone, safety ﬁrst rules utilise at least some of the information the distribution function provides on speciﬁc results and their probabilities.