Calibrating the Subjective

Summary

The paper explores the concept of subjective expected utility (SEU) and its implications on risk aversion. The author conducts a calibration exercise to show that the rejection of some risky bets by a risk-averse agent only implies the rejection of more extreme and less desirable bets.

Highlights

• The paper revisits Rabin's calibration theorem in the context of subjective expected utility (SEU).
• The author shows that the pathologies identified by Rabin vanish in the subjective realm.
• The paper introduces the concept of "actuarial worsening" to describe situations where a risky option becomes less desirable.
• The author constructs a utility function to demonstrate the necessity of actuarial worsening for the safe option to remain optimal.
• The paper proves that if the risky option becomes worse, the safe option must remain optimal.
• The author discusses the implications of the results for situations where the decision-maker prefers the safe option to the risky option for all wealth levels.
• The paper concludes that the SEU paradigm provides a more nuanced understanding of risk aversion.

Key Insights

• The paper challenges the objectivist view of probability and instead adopts a subjective approach, where probabilities are a rate at which an individual is willing to bet on the occurrence of an event.
• The author's calibration exercise reveals that the rejection of some risky bets by a risk-averse agent only implies the rejection of more extreme and less desirable bets, and not a blanket rejection of all risky bets.
• The concept of actuarial worsening is crucial in understanding how a risky option becomes less desirable, and the author shows that this is a necessary condition for the safe option to remain optimal.
• The paper's results have implications for our understanding of risk aversion, suggesting that it is not a fixed trait, but rather a context-dependent phenomenon that depends on the specific options available.
• The author's use of a utility function to demonstrate the necessity of actuarial worsening provides a novel approach to understanding the SEU paradigm.
• The paper's findings highlight the importance of considering the subjective nature of probability when making decisions under uncertainty.
• The author's conclusion that the SEU paradigm provides a more nuanced understanding of risk aversion highlights the need for further research into the subjective nature of decision-making.

Mindmap

Citation

Whitmeyer, M. (2024). Calibrating the Subjective (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.18486