Risk Preferences in Time Lotteries
Yonatan Berman and Mark Kirstein
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Submission date: 15. Feb. 2020 (revised version: September 2021)
MSC-Numbers: 91B06, 91B08, 91B30, 91B74
PACS-Numbers: 89.65.Gh, 05.20.Gg
Keywords and phrases: Ergodicity Economics, Growth-Optimality, Time Lotteries
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Link to arXiv: See the arXiv entry of this preprint.
An important question in economics is how people choose when facing uncertainty in the timing of rewards. In this paper we study preferences over time lotteries, in which the payment amount is certain but the payment time is uncertain. In expected discounted utility (EDU) theory decision makers must be risk-seeking over time lotteries. Here we explore growth-optimality, a normative model consistent with standard axioms of choice, in which decision makers maximise the growth rate of their wealth. Growth-optimality is consistent with both risk-seeking and risk-neutral behaviour in time lotteries, depending on how growth rates are computed. We discuss two approaches to compute a growth rate: the ensemble approach and the time approach. Revisiting existing experimental evidence on risk preferences in time lotteries, we find that the time approach accords better with the evidence than the ensemble approach. Surprisingly, in contrast to the EDU prediction, the higher the ensemble-average growth rate of a time lottery is, the less attractive it becomes compared to a sure alternative. Decision makers thus may not consider the ensemble-average growth rate as a relevant criterion for their choices. Instead, the time-average growth rate may be a better criterion for decision-making.