Risk, Ambiguity, and the Klibanoff Axioms

Machina (2007) formulates a number of experiments, and shows that they can be used to test the Choquet expected utility model. We show that one of them can also be used to test the class of maxmin expected utility preferences in Klibanoff (2001). Those preferences are not consistent with Choquet expected utility preferences in Machina's experiment.maxmin expected utility

Possibility and permissibility

We generalize permissibility (Brandenburger, 1992) to allow for any suitably defined model of preference and definition of possibility. We also prove that the generalized solution concept characterizes rationality, caution, and “common belief" of rationality and caution.

Risk, Ambiguity, and the Klibanoff Axioms

Machina (2007) formulates a number of experiments, and shows that they can be used to test the Choquet expected utility model. We show that one of them can also be used to test the class of maxmin expected utility preferences in Klibanoff (2001). Those preferences are not Choquet expected utility preferences, and they are not consistent with Choquet expected utility preferences in Machina’s experiment.Choquet expected utility,Ellsberg Paradox,Maxmin expected utility,Stochastic independence,Uncertainty

A robust definition of possibility for biseparable preferences

This note presents several preference-based definitions of a likely event, and shows that they induce (in the sense of Lo 2005b) the same set of possible states for biseparable preferences.

Correlated Nash Equilibrium

Nash equilibrium presumes that players have expected utility preferences, and therefore the beliefs of each player are represented by a probability measure. Motivated by Ellsberg-type behavior, which contradicts the probabilistic representation of beliefs, we generalize Nash equilibrium in n-player strategic games to allow for preferences conforming to the maxmin expected utility model of Gilboa and Schmeidler [Journal of Mathematical Economics, 18 (1989), 141–153]. With no strings attached, our equilibrium concept can be characterized by the suitably modified epistemic conditions for Nash equilibrium.Agreeing to disagree, Correlated equilibrium, Epistemic conditions, Knightian uncertainty, Multiple priors, Nash equilibrium

Markov chains and the pricing of derivatives

A numerical method for pricing financial derivatives based on continuous-time Markov chains is proposed. It approximates the underlying stochastic process by a continuous-time Markov chain. We show how to construct a multi-dimensional continuous-time Markov chain such that it converges in distribution to a multi-dimensional diffusion process. The method is flexible enough to be applied to a model where the underlying process contains local volatility, stochastic volatility and jumps. Furthermore, we introduce a method to approximate the dynamics of the realized variance of a Markov chain and an algorithm to reduce the complexity of computing the joint probability distribution between the realized variance and the underlying

A method of storage and display of Chinese characters as graphic symbols

Not provided