Bayesian risk management : "Frequency does not make you smarter"

Within our research group Bayesian Risk Solutions we have coined the idea of a Bayesian Risk Management (BRM). It claims (1) a more transparent and diligent data analysis as well as (2)an open-minded incorporation of human expertise in risk management. In this dissertation we formulize a framework for BRM based on the two pillars Hardcore-Bayesianism (HCB) and Softcore-Bayesianism (SCB) providing solutions for the claims above.For data analysis we favor Bayesian statistics with its Markov Chain Monte Carlo (MCMC) simulation algorithm. It provides a full illustration of data-induced uncertainty beyond classical point-estimates. We calibrate twelve different stochastic processes to four years of CO2 price data. Besides, we calculate derived risk measures (ex ante/ post value-at-risks, capital charges, option prices) and compare them to their classical counterparts.When statistics fails because of a lack of reliable data we propose our integrated Bayesian Risk Analysis (iBRA) concept. It is a basic guideline for an expertise-driven quantification of critical risks. We additionally review elicitation techniques and tools supporting experts to express their uncertainty.Unfortunately, Bayesian thinking is often blamed for its arbitrariness. Therefore, we introduce the idea of a Bayesian due diligence judging expert assessments according to their information content and their inter-subjectivity.