| The dissertation consists of three essays. In the first essay, we examine a general class of non linear self-referential economies in which agents use least squares learning to forecast and update their beliefs, given an arbitrary vector of past state variables and forecasts. We find conditions for which least squares learning converges to adaptive rules. These conditions are similar to conditions found by Grandmont (1985) and Guesnerie & Woodford (1989) for convergence of adaptive rules to stationary equilibria. We further show these conditions enable expectations to be "trained" in the sense of Marimon, Spear, & Sunder (1991).; In the second essay, we examine a representative agent using neural networks to forecast in a single good non-linear, first order self-referential model. We first consider intermediate stage learning, where agents update the forecasting rule every {dollar}tau{dollar} periods. We show that, in theory and simulations, the learning rule does not converge to the rational expectations equilibrium (REE) or to rational bootstrap equilibria. We next consider two-stage learning, where agents learn the functional mapping between the current forecast function and the previous forecast function. We show that, in theory and simulations, the two stage learning rule converges to the REE.; In the third essay, we use a neural network to statistically approximate a valuation function for American put options with real data. The neural network valuation function is twice differentiable, and provides an instantaneous approximation of the American put options using a set of multiple state variables. We use the neural network valuation function to form hedged portfolios for American put options against changes in the stock price, the delta of the stock price, and interest rate. |
