Title: Risk management application of intrinsic discrepancy loss functions
Authors: Zinoviy Landsman - University of Haifa (Israel)
Limor Langbord - University of Haifa (Israel)
Udi Makov - University of Haifa (Israel) [presenting]
Abstract: One of the main problems in risk management is the evaluation of risk measures, which are typically explored for their mathematical properties, under the assumption that all the underlying parameters of the loss distribution are known. In practice, little attention is given to the impact the choice of parameter estimates has on the accuracy of such measures. We propose to estimate these parameters by minimizing the expectation of the intrinsic discrepancy loss function (IDLF), which is the inherent loss function arising only from the underlying distribution, without any external subjective considerations. Firstly, we discuss the intrinsic estimation of the mean of the Tweedie family, which is a subclass of the reproductive exponential dispersion family, a reach family with wide applications in risk management, and provide the IDLF of the family. Secondly, we provide a numerical study of the estimates of the Value at Risk (VaR) and the Tail Conditional Expectation (TCE) of the gamma loss distribution using the IDLF and its approximation.