Economy – Quantitative Finance – Risk Management
Scientific paper
2011-06-30
Economy
Quantitative Finance
Risk Management
Scientific paper
In this paper, we investigate two different frameworks for assessing the risk in a multi-period decision process: a dynamically inconsistent formulation (whereby a single, static risk measure is applied to the entire sequence of future costs), and a dynamically consistent one, obtained by suitably composing one-step risk mappings. We characterize the class of dynamically consistent measures that provide a tight approximation for a given inconsistent measure, and discuss how the approximation factors can be computed. For the case where the consistent measures are given by Average Value-at-Risk, we derive a polynomial-time algorithm for approximating an arbitrary inconsistent distortion measure. We also present exact analytical bounds for the case where the dynamically inconsistent measure is also given by Average Value-at-Risk, and briefly discuss managerial implications in multi-period risk-assessment processes. Our theoretical and algorithmic constructions exploit interesting connections between the study of risk measures and the theory of submodularity and lattice programming, which may be of independent interest.
Huang Pu
Iancu Dan A.
Petrik Marek
Subramanian Dharmashankar
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