Risk measures for income streams

Abstract

A new measure of risk is introduced for a sequence of random incomes adapted to some filtration. This measure is formulated as the optimal net present value of a stream of adaptively planned commitments for consumption. The calculation of the new measure is done by solving a stochastic dynamic linear optimization problem, which, in case of a finite filtration, reduces to a simple deterministic linear program. We show properties of the new measure by exploiting the convexity and duality structure of the stochastic dynamic linear problem. The measure depends on the full distribution of the income process (not only on its marginal distribution) as well as on the filtration, which is interpreted as the available information about the future.