I develop a new method for approximating and estimating nonlinear, non-Gaussian state space models. I show that any such model can be well approximated by a discrete-state Markov process and estimated using techniques developed in Hamilton (1989). Through Monte Carlo simulations, I demonstrate...

A Stochastic Arbitrage Opportunity is defined as a zero-cost investment portfolio that enhances every feasible benchmark portfolio for all admissible utility functions. The present study provides a formal theory of consistent estimation of the set of arbitrage opportunities and an Empirical...

Linking the statistic and the machine learning literature, we provide new general results on the convergence of stochastic approximation schemes and inexact Newton methods. Building on these results, we put forward a new optimization scheme that we call generalized inexact Newton method (GINM)....