The Time Inconsistency Problem

The Time Inconsistency Problem

Statistics

2024

Jy Naha

This study expands upon the work of Barberis (2012) which discusses the application of Tversky and Kahneman’s updated model of prospect theory in 1992 (cumulative prosepect theory) to the area of repeated bets with win probabilities of close to 0.5, in contexts such as casinos or financial markets. In particular, we look to explore the idea of a ’time inconsistency’ that is abundant in many strategic situations evaluated using cumulative prospect theory. What this refers to is the phenomenon of an agent deciding what their optimal strategy is before entering the situation but then following a different plan of action at future time periods. We explore the impacts of moving away from simple bets by changing some of the underlying principles, such as the effects of generalising the win probability, p, or introducing a random shock to the reward at a random point in time. This allows us to connect Barberis’ work to areas beyond just a casino, such as prices of securities in financial markets. We will do this by exploring the effects on a two-period binomial model but which can be extended.

Jy Naha, Decision Theory, Mathematical Finance, Cumulative Prospect Theory, Gambling, Trading, Financial Markets, Statistics, Behavioural Economics, Utility Theory, Game Theory, Optimisation