Quntitative [i.e. Quantitative] analysis of risky decision making in economic environments

Risky economic decisions play an important role in everyone's life. This dissertation presents mathematical approaches to the analysis of these decisions. It discusses how statistical measures can describe properties of choice options, and how these properties can be used to describe the decision context. Also, this dissertation includes a practical tutorial on a Bayesian approach to the hierarchical regression analysis in management science. Therefore, the combined dissertation presents mathematical and statistical tools in, and for better research of, decision making under risk.
The first manuscript proposes standardized covariance, a measure that can quantitatively describe the strength of the association and similarity between choice options' outcomes. The standardized covariance can also describe how risky one option is with respect to another. It can influence predictions of choice models. The second manuscript shows experimentally how association measured with the standardized covariance can influence people's choices. The third manuscript proposes applying the expected shortfall of an option's outcomes as a measure of risk in the standard risk-value models. In an experiment, the risk-value shortfall model successfully predicted people's preference for options with higher expected value, lower variance and more positively skewed distributions of outcomes, and outperformed competing models.
The fourth manuscript proposes a new version of a reinforcement learning model, which can be applied in a social context. The proposed model can account for the behavior of other people competing for a common pool resource. As experimentally tested, the model could successfully predict human behavior and correlated with the brain activity measured with an fMRI method.
The last manuscript outlines advantages of using Bayes factors instead of p-values for interpretation of results from hierarchical regression analysis. As the results in the manuscript show, the Bayesian approach and the standard null-hypothesis statistical testing can lead to different conclusions.