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Indifference pricing with uncertainty averse preferences

Giammarino, Flavia (2011) Indifference pricing with uncertainty averse preferences. PhD thesis, The London School of Economics and Political Science (LSE).

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Abstract

In this dissertation we study the indifference buyer's price and the indifference seller's price of an uncertainty averse decision-maker and the characterization of a decision maker's attitudes toward uncertainty. In the first part of the dissertation we study the properties fulfilled by the indifference buyer's price and by the indifference seller's price of an uncer- tainty averse decision-maker. We find that the indifference buyer's price is a quasiconvex risk measure and that the indifference seller's price is a cash-additive convex risk measure. We identify the acceptance family of the indifference buyer's price as well as the acceptance set of the indifference seller's price. We characterize the dual representations of the indifference buyer's price and of the indifference seller's price both in terms of probabil- ity charges and in terms of probability measures. In the second part of the dissertation we study the characterization of a decision-maker's attitudes toward uncertainty in terms of the indifference buyer's price and of the indifference seller's price. We find that a decision- maker is more uncertainty averse than another if and only if her indifference buyer's price and her indifference seller's price are larger than for the other. We find that a decision-maker is increasingly (respectively, decreasingly, con- stantly) uncertainty averse if and only if her indifference buyer's price and her indifference seller's price are increasing (respectively, decreasing, con- stant) functions of her constant initial wealth. In the last part of the dissertation we further develop the characterization of increasing, decreasing, and constant uncertainty aversion and we derive a technical condition that allows to immediately verify whether an uncer- tainty averse representation of preferences exhibits increasing, decreasing, or constant uncertainty aversion. We find that this technical condition allows 6to classify a large class of uncertainty averse representations of preferences into increasingly, decreasingly, and constantly uncertainty averse.

Item Type: Thesis (PhD)
Additional Information: © 2011 Flavia Giammarino
Library of Congress subject classification: H Social Sciences > HG Finance
Sets: Departments > Statistics
Supervisor: Barrieu, Pauline
URI: http://etheses.lse.ac.uk/id/eprint/209

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