This paper introduces a (coherent) risk measure that describes the uncertainty of the model (represented by a probability measure P) by a set P of probability measures each of which has a Radon-Nikodym's derivative (with respect to P) that lies within the interval [; 1/] for some constant (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.
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