Optimal intertemporal risk allocation with applications to finance and insurance

井上、中野和福田在跨期风险分配上得出了不同的结果。在指数效用的情况下，他们发现，当被视为动态风险度量时，这样获得的保费原则变得时间一致。井上引入了跨期风险分配的均衡，并将Buhlmann和Esscher原理推广到这种情况。Inoue和Kasahara将只在一维情况下发展起来的动态依赖结构分析的预测理论方法推广到了多变量情况。更准确地说，他们采用离散时间过程的基本情况，并将一维情况下的各种结果推广到多变量情况。

Inoue, Nakano and Fukuda obtained various results on the intertemporal risk allocation. In the case of exponential utility, they found that the premium principle thus obtained becomes time-consistent when viewed as a dynamic risk measure. Inoue introduced the equilibrium for the intertemporal risk allocation, and extended the Buhlmann and Esscher principles to this case. Inoue and Kasahara extended the prediction-theoretic method for the analysis of dynamic dependence structure, which had been developed only in the one-dimensional case, to the multivariate case. More precisely, they took the fundamental case of discrete-time processes, and extended various results in the one-dimensional case to the multivariate case.