Comparing financial investments by their state dependent returns: A one-way log utility representation
In a standard single-period model under risk, we formalize and discuss an intuitive criterion for the binary comparison of financial investments. Two investments - x and y - are compared by calculating the present value of x's payoffs using the state dependent returns of y as discount factors. The induced preference is asymmetric but exhibits intransitive indifference. If the feasible set is convex, then the criterion selects a unique maximum element. Interestingly, it can be shown that the induced preference can be represented by a one-way expected utility representation employing logarithmic utility. Besides giving a relevant and illustrative example for a one-way utility representation, this result provides a new interpretation of using logarithmic utility for expected utility based decision-making.
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- Speckbacher, Gerhard, 1998. "Maintaining capital intact and WARP," Mathematical Social Sciences, Elsevier, vol. 36(2), pages 145-155, September.
- Fishburn, Peter C, 1991. "Nontransitive Preferences in Decision Theory," Journal of Risk and Uncertainty, Springer, vol. 4(2), pages 113-134, April.
- Hellwig, K. & Speckbacher, G. & Wentges, P., 2000. "Utility maximization under capital growth constraints," Journal of Mathematical Economics, Elsevier, vol. 33(1), pages 1-12, February.
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