Essays on risk and uncertainty in financial decision making: Bayesian inference of multi-factor affine term structure models and dynamic optimal portfolio choices for robust preferences
This thesis studies model inference about risk and decision making under model uncertainty in two specific settings. The first part of the thesis develops a Bayesian Markov Chain Monte Carlo (MCMC) estimation method for multi-factor affine term structure models. Affine term structure models are popular because they provide closed-form solutions for the valuation of fixed income securities. Efficient estimation methods for parameters of these models, however, are not readily available. The MCMC algorithms developed provide more accurate estimates, compared with alternative estimation methods. The superior performance of the MCMC algorithms is first documented in a simulation study. Convergence of the algorithm used to sample posterior distributions is documented in numerical experiments. The Bayesian MCMC methodology is then applied to yield data. The in-sample pricing errors obtained are significantly smaller than those of alternative methods. A Bayesian forecast analysis documents the significant superior predictive power of the MCMC approach. Finally, Bayesian model selection criteria are discussed. Incorporating aspects of model uncertainty for the optimal allocation of risk has become an important topic in finance. The second part of the thesis considers an optimal dynamic portfolio choice problem for an ambiguity-averse investor. It introduces new preferences that allow the separation of risk and ambiguity aversion. The novel representation is based on generalized divergence measures that capture richer forms of model uncertainty than traditional relative entropy measures. The novel preferences are shown to have a homothetic stochastic differential utility representation. Based on this representation, optimal portfolio policies are derived using numerical schemes for forward-backward stochastic differential equations. The optimal portfolio policy is shown to contain new hedging motives induced by the investor's attitude toward model uncertainty. Ambiguity concerns introduce additional horizon effects, boost effective risk aversion, and overall reduce optimal investment in risky assets. These findings have important implications for the design of optimal portfolios in the presence of model uncertainty.
Thesis (Ph.D.)--Boston University