Center for Mathematical Economics Working Papers No. 609
This paper introduces a (coherent) risk measure that describes the uncertainty of the model (represented by a probability measure P₀) by a set Pᵧ of probability measures each of which has a Radon-Nikodym's derivative (with respect to P₀) that lies within the interval [λ; 1/λ] for some constant λ ϵ (0,1]. Economic considerations are discussed and an explicit representation is obtained that gives a connection to both the expected loss of the financial position and its average value-at-risk. Optimal portfolio analysis is performed - different optimization criteria lead to Merton portfolio. Comparison with related problems reveals examples of extreme sensitivity of optimal portfolios to model parameters and the choice of risk measure.
Risk measure Model uncertainty Value at risk Average value at risk Optimal portfolio Merton portfolio