In the post-crisis era, financial institutions seem to be more aware of the risks posed by extreme events. Even though there are attempts to adapt methodologies drawing from the vast academic literature on the topic, there is also skepticism that fat-tailed models are needed. In this paper, we address the common criticism and discuss three popular methods for extreme risk modeling based on full distribution modeling and and extreme value theory.

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The prospect theory value function is modified to make it consistent with rational dynamic asset pricing theory.n A new probability weighting function consistent with rational dynamic asset pricing theory and the corresponding option pricing formula are derived.n The new prospect theory value functions and probability weighting functions show possible extensions of the classical prospect theory and cumulative prospect theory.

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