A time-varying quantile can be fitted by formulating a time series model for the corresponding population quantile and iteratively applying a suitably modified state space signal extraction algorithm. It is shown that such quantiles satisfy the defining property of fixed quantiles in having the appropriate number of observations above and below. Like quantiles, time-varying expectiles can be estimated by a state space signal extraction algorithm and they satisfy properties that generalize the moment conditions associated with fixed expectiles. Because the state space form can handle irregularly spaced observations, the proposed algorithms can be adapted to provide a viable means of computing spline-based non-parametric quantile and expectile regressions

The basic concepts and tools for the Quantitative Probabilistic Risk Analysis are presented.The rationale of the risk acceptability criteria is discussed in the case of rail tunnel safety in Italy.

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Term structure of interest rates, Sequential Monte Carlo method, Importance sampling,

KEY FINDINGSn Machine learning (ML) methods have several advantages that can lead to successful applications in active portfolio management, including the ability to capture nonlinear patterns and a focus on prediction through ensemble learning.n ML methods can be applied to different steps of the investment process, including signal generation, portfolio construction, and trade execution, with reinforcement learning expected to play a more significant role in the industry.n Empirically, the investment performance of ML-based active exchange-traded funds is mixed.