We develop a mathematical proof demonstrating that only financially-strong firms will sell put options on their own stock, but financially-weak firms will not. The sale of options on a company's own stock exposes the buyer to default risk of the issuer, which additionally complicates the payoff...

This paper considers multiple market agents who have distinct distributional opinions about the state price density. We first determine the optimal trading positions of a utility maximizing market taker who trades Arrow-Debreu securities for prices set by the market maker. We use calculus of...

Linear Methods are often used to compute approximate solutions to dynamic models, as these models often cannot be solved analytically. Linear methods are very popular, as they can easily be implemented. Also, they provide a useful starting point for understanding more elaborate numerical...

I introduce and evaluate a new stochastic simulation method for dynamic economic models. It is based on recent work in the operations research and engineering literatures (Van Roy et. al, 1997; Powell, 2007; Bertsekas, 2011). The baseline method involves rewriting the household's dynamic program in...

This research examines the computational complexity of two boundedly rational choice models that use multiple rationales to explain observed choice behavior. First, we show that the notion of rationalizability by K rationales as introduced by Kalai, Rubinstein, and Spiegler (2002) is NP-complete...

We consider a setting where a coalition of individuals chooses one or several alternatives from each set in a collection of choice sets. We examine the computational complexity of Pareto rationalizability. Pareto rationalizability requires that we can endow each individual in the coalition with...

This paper addresses the joint calibration problem of SPX options and VIX options or futures. We show that the problem can be formulated as a semimartingale optimal transport problem under a finite number of discrete constraints, in the spirit of [arXiv:1906.06478]. We introduce a PDE...

In this paper, we introduce and develop the theory of semimartingale optimal transport in a path dependent setting. Instead of the classical constraints on marginal distributions, we consider a general framework of path dependent constraints. Duality results are established, representing the...

We propose a new method for solving high-dimensional dynamic programming problems and recursive competitive equilibria with a large (but finite) number of heterogeneous agents using deep learning. The "curse of dimensionality" is avoided due to four complementary techniques: (1) exploiting...

We provide a survey of recent results on model calibration by Optimal Transport. We present the general framework and then discuss the calibration of local, and local-stochastic, volatility models to European options, the joint VIX/SPX calibration problem as well as calibration to some...