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 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 Kreps' (2019) conjecture that optimal expected utility in the classic Black–Scholes–Merton (BSM) economy is the limit of optimal expected utility for a sequence of discrete-time economies that “approach” the BSM economy in a natural sense: The nth discrete-time economy is...

The problem of choosing an optimal toolkit day after day, when the distribution of values of different toolkits is uncertain and can only be observed by carrying different toolkits, is a multi-armed bandit problem with non-independent arms. Accordingly, except for very simple specifications,...

This paper continues our study of heuristics employed to choose dynamically tools to put in a toolkit, where the value of any tool can be discovered only by choosing it. This is a multi-armed bandit problem with “arms” that are not independent, hence it is a problem for which the optimal...