2009-07-24Buch DOI: 10.18452/8403
The role of information in multi-period risk measurement
Multi-period risk functionals assign a risk value to a discrete-time stochasticprocess $Y = (Y_1 , . . . , Y_T )$. While convexity and monotonicity properties extend ina natural way from the single-period case and several types of translation properties may be deﬁned, the role of information becomes crucial in the multi-period situation. In this paper, we deﬁne multi-period functionals in a generic way, such that the available information (expressed as a ﬁltration) enters explicitly the deﬁnition of the functional. This allows to study the information monotonicity property,which comes as the counterpart of value monotonicity. We discuss several ways ofconstructing concrete and computable functionals out of conditional risk mappingsand single-period risk functionals. Some of them appear as value functions of multistage stochastic programs, where the ﬁltration appears in the non-anticipativity constraint. This approach leads in a natural way to information monotonicity. Thesubclass of polyhedral multi-period risk functionals becomes important for theiremployment in practical dynamic decision making and risk management. On the other hand, several functionals described in literature are not information-monotone, which limits their practical use.
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