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This paper investigates the multi-dimensional risk spillover effects of carbon markets with energy, non-energy commodity and stock markets in China before and after the COVID-19 outbreak, through the DY network with GARCHSK-VaR method. The empirical results denote that the total bidirectional risk spillovers of carbon markets become larger after the COVID-19 outbreak than before the COVID-19 outbreak. Interestingly, in both periods, energy is the largest risk contributor to carbon markets, while carbon markets become the net risk contributors to stock markets under COVID-19. Furthermore, compared with Guangdong pilot, the impacts of Hubei pilot on other markets are stronger in both periods. Finally, the dynamic risk spillover effects have obvious differences between before and after the COVID-19 outbreak. [ABSTRACT FROM AUTHOR]

The problem of risk update is one of the core problems of dynamic risk analysis. As for updating widely used probabilistic risk, it's a kind of special problem of pattern recognition which means to transfer from old pattern to new pattern with new information. Aiming at updating probabilistic risk only with the new observations and without the original observations, this paper proposes the morphogenetic updating algorithm to update the probabilistic risk with only new observations and old risk values by reproducing the morphogenesis of new observations and old risk values based on morphogenetic estimation. The form rules hidden in the risk values and new observations are discovered by internal source in Write operation, and the projection of the input and the cosine similarity measure as the basis for defining the weight of updating are computed in Read operation. Based on Resconi theorem, the input is reproduced by its projection on the context which provides the same mathematical space for updating and stores the structural information hidden in the risk. By applying the algorithm to updating the probabilistic risk of typhoon rainstorms occurred in Guangdong Province, it proves that morphogenetic updating algorithm provides us a method to updating probabilistic risk fast and satisfactorily and it's a sustainable updating method which can be used for dynamic risk analysis. [ABSTRACT FROM AUTHOR]