| Summary: | This dissertation is comprised of four essays. It develops statistical models of decision making in the presence of risk with applications to economics and finance. The methodology draws upon economics, finance, psychology, mathematics and statistics. Each essay contributes to the literature by either introducing new theories and empirical predictions or extending old ones with novel approaches .The first essay (Chapter II) includes, to the best of our knowledge, the first known limit distribution of the myopic loss aversion (MLA) index derived from micro-foundations of behavioural economics. That discovery predicts several new results. We prove that the MLA index is in the class of α-stable distributions. This striking prediction is upheld empirically with data from a published meta-study on loss aversion; published data on cross-country loss aversion indexes; and macroeconomic loss aversion index data for US and South Africa. The latter results provide contrast to Hofstede's cross-cultural uncertainty avoidance index for risk perception. We apply the theory to information based asset pricing and show how the MLA index mimics information flows in credit risk models. We embed the MLA index in the pricing kernel of a behavioural consumption based capital asset pricing model (B-CCAPM) and resolve the equity premium puzzle. Our theory predicts: (1) stochastic dominance of good states in the B-CCAPM Markov matrix induce excess volatility; and (2) a countercyclical fourfold pattern of risk attitudes. The second essay (Chapter III) introduces a probability model of "irrational exuberance "and financial market instability implied by index option prices. It is based on a behavioural empirical local Lyapunov exponent (BELLE) process we construct from micro-foundations of behavioural finance. It characterizes stochastic stability of financial markets, with risk attitude factors in fixed point neighbourhoods of the probability weighting functions implied by index option prices. It provides a robust early warning system for market crash across different credit risk sources. We show how the model would have predicted the Great Recession of 2008. The BELLE process characterizes Minskys financial instability hypothesis that financial markets transit from financial relations that make them stable to those that make them unstable.
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