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Christian Hugo Hoffmann undermines the citadel of risk assessment and management, arguing that classical probability theory is not an adequate foundation for modeling systemic and extreme risk in complex financial systems. He proposes a new class of models which focus on the knowledge dimension by precisely describing market participants' own positions and their propensity to react to outside changes. The author closes his thesis by a synthetical reflection on methods and elaborates on the meaning of decision-making competency in a risk management context in banking. By choosing this poly-dimensional approach, the purpose of his work is to explore shortcomings of risk management approaches of financial institutions and to point out how they might be overcome.