Locally Constant Model Uncertainty Risk Measure

Obradovic L. Locally Constant Model Uncertainty Risk Measure. Center for Mathematical Economics Working Papers. Vol 609. Bielefeld: Center for Mathematical Economics; 2019.This paper introduces a (coherent) risk measure that describes the uncertainty of the model (represented by a probability measure $P_0$) by a set $P_\lambda$ of probability measures each of which has a Radon-Nikodym's derivative (with respect to $P_0$) that lies within the interval $[\lambda,\frac{1}{\lambda}]$ for some constant $\lambda\in(0,1]$. 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