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No trade in financial markets with uncertainty.
Abstract
In this paper a Radner economy is considered with Uncertainty, modeled by means of the Choquet Expected Utility. Agents are split into two categories: optimists, who hold a concave capacity, and pessimists, who hold a convex one. A no trade theorem is stated and proved under the assumption of common beliefs with uncertainty.
... The optimistic decision-maker considers the ask price of the asset β as the lowest price (upper bound) at which she will wish to sell the asset, consistent with her priors. She considers the bid price of the asset β as the highest price (lower bound) up to which she will wish to buy the asset β, compatible with her beliefs (Basili and Fontini, 2002). Summing up, the decision-maker assumes that the true probability distribution of the asset β payments is located in the set P of probability 5 We suppose that optimists (pessimists) hold concave (convex) capacities. ...
Real investments involving irreversibility and ambiguity embed a positive quasi-option value under ambiguity (q.o.v.a.), which modifies the evaluation of an investment decision involving depletion of natural resources by increasing the value of delaying. Q.o.v.a. depends on the specific decision-maker attitude towards ambiguity, expressed by a capacity on the state space. An empirical measure of q.o.v.a. is pointed out. Exploiting the properties of a capacity and its conjugate, the relationship has been established between the upper and lower Choquet integral with respect to a subadditive capacity and the bid and ask price of the underlying asset (output) of the investment decision. The empirical measure of q.o.v.a. is defined as the upper bound of the opportunity value. As an example, q.o.v.a. is applied to evaluate an off-shore petroleum lease under ambiguity.
We develop a Savage-type model of choice under uncertainty in which agents identify uncertain prospects with subjective compound lotteries. Our theory permits issue preference; that is, agents may not be indifferent among gambles that yield the same probability distribution if they depend on different issues. Hence, we establish subjective foundations for the Anscombe-Aumann framework and other models with two different types of probabilities. We define second-order risk as risk that resolves in the first stage of the compound lottery and show that uncertainty aversion implies aversion to second-order risk which implies issue preference and behavior consistent with the Ellsberg paradox.