Measuring risk for income streams

Georg Ch Pflug, Andrzej Ruszczyński

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


A 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 new measure is calculated by solving a stochastic dynamic linear optimization problem which, for finite filtrations, reduces to a deterministic linear programming problem. We analyze 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 distributions) as well as on the filtration, which is interpreted as the available information about the future. The features of the new approach are illustrated by a numerical example.

Original languageEnglish (US)
Pages (from-to)161-178
Number of pages18
JournalComputational Optimization and Applications
Issue number1-2
StatePublished - Oct 2005

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics


  • Conditional value at risk
  • Dynamic risk measure
  • Multiperiod mean-risk models
  • Multistage stochastic programming
  • Value of perfect information


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