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  • Risk Management in Insurance and Finance in Response to Model Uncertainty
    (2024) Yang, Yunshen
    Thesis
    The world we live in is rapidly evolving and full of complexity, compounded by emerging threats due to climate change and shocks such as COVID-19. These factors impose existential challenges on the insurance and financial industries, calling for refined risk management tools. This thesis focuses on one specific challenge, model uncertainty, a notorious issue that is pervasive in virtually all applied fields and is exacerbated in this changing environment. I endeavour to develop a series of approaches to address the issue of model uncertainty in risk assessment, portfolio management, and financial decision-making. First, consider a general problem of estimating the expectation of a certain loss function, where the underlying probability distribution is unknown. The objective is subject to an ambiguity issue, for which the worst-case treatment has been developed in the literature but the resulting estimates are often too conservative. We propose a scenario analysis and develop a new worst-case treatment. As an illustration, we derive worst-case moment estimates analytically. Our numerical results show that our approach indeed greatly alleviates the over-conservativeness issue. Next, we examine large investment portfolios that are crucially important for social and economic security. Consider a portfolio exposed to multilevel risks, including idiosyncratic risk, systematic risk, and common shock. In this changing environment, we argue that common shock and systematic risk, which are usually assumed to be independent in the literature, may interplay with each other, forming a causal loop and leading to a joint extreme scenario. An asymptotic study of the portfolio loss due to defaults is carried out under a joint regular variation structure of common shock and systematic risk. Our main finding is that the tail dependence between these two risk factors, besides their marginal tails, is another driving force in the portfolio loss. Lastly, we investigate how humans make financial forecasts under Knightian uncertainty. Our hypothesis posits that a little information nudge can empower humans to surmount Knightian uncertainty independently, thereby greatly improving their performance. To test this, we design an innovative experiment in which participants forecast structural shifts in the market and then compare the results from three experimental treatments with varying degrees of information nudges. The data collected so far strongly supports our hypothesis.