The Value-at-Risk (VaR) and the Expected Shortfall (ES) are the two most
popular risk measures in banking and insurance regulation. To bridge between
the two regulatory risk measures, the Probability Equivalent Level of VaR-ES
(PELVE) was recently proposed to convert a level of VaR to that of ES. It is
straightforward to compute the value of PELVE for a given distribution model.
In this paper, we study the converse problem of PELVE calibration, that is, to
find a distribution model that yields a given PELVE, which may either be
obtained from data or from expert opinion. We discuss separately the cases when
one-point, two-point, n-point and curve constraints are given. In the most
complicated case of a curve constraint, we convert the calibration problem to
that of an advanced differential equation. We apply the model calibration
techniques to estimation and simulation for datasets used in insurance. We
further study some technical properties of PELVE by offering a few new results
on monotonicity and convergence.