We examine the connection between discrete-time models of financial markets and the celebrated Black--Scholes--Merton (BSM) continuous-time model in which "markets are complete." We prove that if (a) the probability law of a sequence of discrete-time models converges to the law of the BSM model,...

We examine the connection between discrete-time models of financial markets and the celebrated Black--Scholes--Merton (BSM) continuous-time model in which ''markets are complete." Suppose that (a) the probability law of a sequence of discrete-time models converges to the law of the BSM model and...

We derive a simplified version of the model of Fudenberg and Levine [2006, 2011] and show how this approximate model is useful in explaining choice under risk. We show that in the simple case of three outcomes, the model can generate indifference curves that “fan out” in the Marshack-Machina...

We develop a dual-self model of self-control that is compatible with modern dynamic macroeconomic theory and evidence. We show that a convex cost of self-control explains a wide range of behavioral anomalies concerning risk, including the Allais paradox, and also explains the observed...