Adequate Decision Rules for Portfolio Choice Problems by T. Goodall

By T. Goodall

The writer offers the speculation of portfolio selection from a brand new viewpoint, recommending determination ideas that experience benefits over these presently utilized in thought and perform. Portfolio selection conception is dependent upon anticipated values. Goodall argues that this dependence has a ancient foundation and argues that present choice principles are insufficient for many portfolio selection occasions. Drawing on econometric recommendations proposed for the matter of forecasting results of an opportunity test, the writer defines adequacy standards, and proposes enough choice principles for numerous situations.

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For gambles repeated finitely often, there is no reason to believe that the accumulated net gain fluctuates around zero. 18 For the St Petersburg game, no finite expected value exists, and the law of large numbers is inapplicable. It is thus impossible to derive the ‘fair’ entrance fee to the St Petersburg game from the law of large numbers, on which the expected gain rule rests. 19 This would induce an entirely different decision situation, of course, and so does not remedy the expected gain rule’s inapplicability to the St Petersburg game.

The unfortunate lack of distinction between ϕ(u) and u(r) by von Neumann and Morgenstern, and their equally unfortunate choice of wording, has led to two different kinds of misinterpretation. First, it has led to claims that the EU principle was identical to Bernoulli’s ‘moral expectation’ rule. 25 Of course, the two are not identical at all, unless ω(r) is defined being equal to ln(r). Second, it has led to claims that the EU principle was identical to Bayes’s rule. This may be correct with regard to their mathematical form, since u(r) and ω(r) are mathematically indistinguishable.

Telser (1955/56) and Kataoka (1963) proposed two more safety first rules for portfolio choice settings. Because of their emphasis on disastrous occurrences, safety first rules have always lent themselves to appeals to intuition and introspection. Their application to problems of decision under Knightian risk was thus almost always justified on rather behavioural reasoning. It might thus be argued that they should only be treated as descriptive decision rules. As such they have indeed been tested empirically, mainly in studies where behaviour under potential crisis results was analysed.

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