Survival under Uncertainty by Dimitri Volchenkov

Author:Dimitri Volchenkov
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(6.33)

where is the risk tolerance parameter—as decreases, traders become more risk-averse and vice versa. In the limit of maximum risk avoidance, and the function (6.33) turns into the Bernoulli logarithmic utility function [141],

(6.34)

Let us consider a population characterized by some distribution of wealth p w . The expected utility over the population is

(6.35)

According to the maximum entropy principle [29, 30], the system would evolve toward the state of maximum entropy characterized by the probability distribution which can be achieved in the largest number of ways, this being the most likely distribution to be observed. We are interested in the probability distribution of wealth p w over the population with maximum entropy:

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