Some Improvements on Minimum Information Bivariate Copula to Analyze Liability Claims: the Indemnity Payment and the Allocated Loss Adjustment Expense

Minimum information copula provides parametric class of copula which have good levels of approximation, to any required degree of precision. It can be quantified, either in terms of expert judgment or data itself. The only technical assumptions should be made are that the multivariate copula density under study is continuous and non-zero, and no other assumptions are needed. The purpose of the presented paper is two folds: from one sides, doing minimum information copula is required to discretize or grid desired variables that has always be considered as a uniform grid. Here, we are going to investigate influence of different grids such as Chebyshev and Halton on the approximation accuracy. Since, for example, Chebyshev points allow more points in the tail or boundaries of our approximation which are very important especially in financial and actuarial applications. On the other, Lagrange multiplayers in minimum information copula should be determined which depends on expected values of the constraint in a nonlinear way. One of the possible solvers for this task would be FMINSEARCH - MATLAB’s optimization routine, which implemented using the Nelder-Mead simplex method. In this paper, another root finding techniques FMINUNC is used which is extremely more useful/powerful as compared to FMINSEARCH in finding minimum information copula. The results gained show that our considered changes lead to better copula approximation. Finally, we apply our improved minimum information method to analyze general liability claims that randomly chosen from late settlement lags and were supplied by Insurance Services Office, Inc. For each claim, the indemnity payment (LOSS) and the allocated loss adjustment expense (ALAE) were recorded.