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Recursiveness of indifference prices and translation-invariant preferences

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Abstract

We consider an economic agent with dynamic preferences over a set of uncertain monetary payoffs. We assume that preferences are updated in a time-consistent way as more information is becoming available. Our main result is that the agent’s indifference prices are recursive if and only if the preferences are translation-invariant. The proof is based on a characterization of time-consistency of dynamic preferences in terms of indifference sets. As a special case, we obtain that expected utility leads to recursive indifference prices if and only if absolute risk aversion is constant, that is, the Bernoulli utility function is linear or exponential.

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Authors and Affiliations

  1. Princeton University, Princeton, NJ, 08544, USA

    Patrick Cheridito

  2. Vienna Institute of Finance, 1190, Vienna, Austria

    Michael Kupper

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  1. Patrick Cheridito
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  2. Michael Kupper
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Correspondence to Patrick Cheridito.

Additional information

An earlier version of this paper was titled “Time-consistent indifference prices and monetary utility functions”. We thank Freddy Delbaen and Faruk Gul for helpful comments. Patrick Cheridito was supported by NSF grant DMS-0642361. Michael Kupper was supported by the Swiss National Science Foundation and Vienna Science and Technology Fund.

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Cheridito, P., Kupper, M. Recursiveness of indifference prices and translation-invariant preferences. Math Finan Econ 2, 173–188 (2009). https://doi.org/10.1007/s11579-009-0020-3

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  • DOI: https://doi.org/10.1007/s11579-009-0020-3

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