Rationalizing Investors Choice
Carole Bernard (University of Waterloo, Canada)
Joint work with Jit Seng Chen and Steven Vanduffel

Tuesday June 3, 16:30-17:00 | session 3.7 | Utility | room I

Assuming that agents' preferences satisfy first-order stochastic dominance, we show how the Expected Utility setting with a concave utility can rationalize all optimal investment choices: the optimal investment strategy in any behavioral law-invariant (state-independent) setting corresponds to the optimum for an expected utility maximizer with an explicitly derived concave non-decreasing utility function. This result enables us to infer the utility and risk aversion of agents from their investment choice in a non-parametric way. We relate the property of decreasing absolute risk aversion (DARA) to distributional properties of the terminal wealth and the financial market. Specifically, we show that DARA is equivalent to a demand for a terminal wealth that has more spread than the opposite of the log pricing kernel at the investment horizon.

Cost-Efficient Contingent Claims under Knightian Uncertainty: A Distributional Analysis
Mario Ghossoub (Imperial College London, UK)

Tuesday June 3, 17:00-17:30 | session 3.7 | Utility | room I

In complete frictionless securities markets under uncertainty, it is well-known that in the absence of arbitrage opportunities, there exists a unique linear positive pricing rule, which induces a state-price density. Dybvig (1988) showed that the cheapest way to acquire a certain distribution of a consumption bundle (or security) is when this bundle is anti-comonotonic with the state-price density, i.e., arranged in reverse order of the state-price density. In this paper, we examine a related problem. We consider an investor in a securities market where the pricing rule is 'law-invariant' with respect to a capacity, e.g., a Choquet integral with respect to a capacity as in Cerreia-Vioglio et al. (2012). The investor holds an asset with a random price X and his problem is that of buying the cheapest contingent claim Y on X, subject to some constraints on the performance of the contingent claim and on its level of risk exposure. The cheapest such claim is called cost-efficient. If the capacity satisfies standard continuity and a property called strong diffuseness, we show the existence of a cost-efficient claim, and we show that a cost-efficient claim is anti-comonotonic with the underlying asset's price X. Strong diffuseness is satisfied by a large collection of capacities, including all distortions of diffuse probability measures. As an illustration, we consider the case of a Choquet pricing functional with respect to a capacity (as in Cerreia-Vioglio et al. (2012)) and the case of a Choquet pricing functional with respect to a distorted probability measure. Finally, we consider a simple example in which we derive an explicit form for a cost-efficient claim.