No-Betting Pareto Optima
A talk in the Mathematical finance / Insurance mathematics series by
Mario Ghossoub from University of Waterloo
| Abstract: | In a pure-exchange economy with no aggregate uncertainty, when will two economic agents want to bet (engage in speculative trade), thereby introducing uncertainty into the economy? When the agents are risk-averse Expected-Utility (EU) maximizers, it is well-known that betting is Pareto-improving if and only if the agents have heterogeneous beliefs. In this talk, I will re-visit this problem in two situations: (1) One agent has EU preferences, the other agent has Rank-Dependent Utility (RDU) preferences with a general probability distortion function, and allowing for any type or level of belief heterogeneity; and (2) both agents are RDEU-maximizers, with different distortions of the same probability measure. In both situations, we characterize in closed-form and in full generality Pareto-optimal allocations between the two agents, and we derive a necessary and sufficient condition for Pareto-optima to be no-betting allocations (i.e., deterministic allocations). We find, among other things, that in case (1) common beliefs might still lead to a risk-sharing situation in which betting is Pareto-improving; and betting might not always be Pareto-improving when beliefs are divergent. Furthermore, in case (2), it is the difference in probabilistic risk attitudes given common beliefs, rather than heterogeneity or ambiguity in beliefs, that is a driver of betting behavior. As by-product of our analysis, we answer the question of when sunspots matter in this economy. Zoom Meeting ID: 95930746952 Passcode: 098268 |