Value-at-Risk (VaR) and Expected Shortfall (ES) are common high quantile-based risk measures adopted in financial … regulations and risk management. In this paper, we propose a tail risk measure based on the most probable maximum size of risk … events (MPMR) that can occur over a length of time. MPMR underscores the dependence of the tail risk on the risk management …

. Based on the empirical evidence presented in this paper, our framework offers more realistic portfolio risk measures and a … more tractable method for portfolio optimization. -- portfolio risk ; portfolio optimization ; portfolio budgeting …

literature. First, a numerically more stable objective function for the estimation of the risk neutral density is derived whose …. -- option implied probability of default ; risk neutral density ; cross entropy …

explicit expressions for the bounds.The semiparametric bounds are useful in risk analysis where there is only incomplete … bounds leads to approximations to bounds on Value at Risk (VaR). Besides helping to construct a representative distribution … with given moments, the moment-constrained maximum-entropy method can be used to define risk neutral probabilities for …

Extreme value theory for a class of EGARCH processes is developed. It is shown that the EGARCH process as well as the … results are then compared to related models, such as stochastic volatility models or Log-ACD models. -- EGARCH ; exponential … GARCH ; extreme value theory ; tail behavior ; Gumbel distribution ; conditional variance ; Gaussian tail ; stochastic …

these events. Using theory and simulations we study the implications of the imminent threat of climate change on different … that lead to these assets becoming stranded. Our result suggest that climate change implies a positive and increasing risk … premium, with the overall equity premium depending on the volatility of the stochastic process that governs climate change …