scholarly journals Portfolio Selection by the Axiom of Choice: Post Mean-Variance Analysis

2021 ◽  
Vol 26 (2) ◽  
pp. 303
Author(s):  
K. Paul Yoon ◽  
Mohammad Sedaghat ◽  
Gyutai Kim
Keyword(s):  
Portfolio Selection ◽  
Axiom Of Choice ◽  
Variance Analysis ◽  
The Axiom Of Choice ◽  
Mean Variance

The Axiom of Choice Machine

2018 ◽  
Author(s):  
Alexander R. Pruss
Keyword(s):  
Set Theory ◽  
Laws Of Nature ◽  
Axiom Of Choice ◽  
Dutch Book ◽  
The Axiom Of Choice

This is a mainly technical chapter concerning the causal embodiment of the Axiom of Choice from set theory. The Axiom of Choice powered a construction of an infinite fair lottery in Chapter 4 and a die-rolling strategy in Chapter 5. For those applications to work, there has to be a causally implementable (though perhaps not compatible with our laws of nature) way to implement the Axiom of Choice—and, for our purposes, it is ideal if that involves infinite causal histories, so the causal finitist can reject it. Such a construction is offered. Moreover, other paradoxes involving the Axiom of Choice are given, including two Dutch Book paradoxes connected with the Banach–Tarski paradox. Again, all this is argued to provide evidence for causal finitism.

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