A limit distribution of credit portfolio losses with low default probabilities

This paper employs a multivariate extreme value theory (EVT) approach to study the limit distribution of the loss of a general credit portfolio with low default probabilities. A latent variable model is employed to quantify the credit portfolio loss, where both heavy tails and tail dependence of the latent variables are realized via a multivariate regular variation (MRV) structure. An approximation formula to implement our main result numerically is obtained. Intensive simulation experiments are conducted, showing that this approximation formula is accurate for relatively small default probabilities, and that our approach is superior to a copula-based approach in reducing model risk.     

Confidence sets and confidence bands for a beta distribution with applications to credit risk management

Incorporating statistical multiple comparisons techniques with credit risk measurement, a new methodology is proposed to construct exact confidence sets and exact confidence bands for a beta distribution. This involves simultaneous inference on the two parameters of the beta distribution, based upon the inversion of Kolmogorov tests. Some monotonicity properties of the distribution function of the beta distribution are established which enable the derivation of an efficient algorithm for the implementation of the procedure. The methodology has important applications to financial risk management. Specifically, the analysis of loss given default (LGD) data are often modeled with a beta distribution. This new approach properly addresses model risk caused by inadequate sample sizes of LGD data, and can be used in conjunction with the standard recommendations provided by regulators to provide enhanced and more informative analyses.     

Quantile regression for modelling distributions of profit and loss

Quantile regression is applied in two retail credit risk assessment exercises exemplifying the power of the technique to account for the diverse distributions that arise in the financial service industry. The first application is to predict loss given default for secured loans, in particular retail mortgages. This is an asymmetric process since where the security (such as a property) value exceeds the loan balance the banks cannot retain the profit, whereas when the security does not cover the value of the defaulting loan then the bank realises a loss. In the light of this asymmetry it becomes apparent that estimating the low tail of the house value is much more relevant for estimating likely losses than estimates of the average value where in most cases no loss is realised. In our application quantile regression is used to estimate the distribution of property values realised on repossession that is then used to calculate loss given default estimates. An illustration is given for a mortgage portfolio from a European mortgage lender. A second application is to revenue modelling. While credit issuing organisations have access to large databases, they also build models to assess the likely effects of new strategies for which, by definition, there is no existing data. Certain strategies are aimed at increasing the revenue stream or decreasing the risk in specific market segments. Using a simple artificial revenue model, quantile regression is applied to elucidate the details of subsets of accounts, such as the least profitable, as predicted from their covariates. The application uses standard linear and kernel smoothed quantile regression.     

Optimal portfolio for a defined-contribution pension plan under a constant elasticity of variance model with exponential utility

Based on the Lie symmetry method, we derive the explicit optimal invest strategy for an investor who seeks to maximize the expected exponential (CARA) utility of the terminal wealth in a defined-contribution pension plan under a constant elasticity of variance model. We examine the point symmetries of the Hamilton-Jacobi-Bellman (HJB) equation associated with the portfolio optimization problem. The symmetries compatible with the terminal condition enable us to transform the (2+ 1)-dimensional HJB equation into a (1+ 1)-dimensional nonlinear equation which is linearized by its infinite-parameter Lie group of point transformations. Finally, the ansatz technique based on variables separation is applied to solve the linear equation and the optimal strategy is obtained. The algorithmic procedure of the Lie symmetry analysis method adopted here is quite general compared with conjectures used in the literature.     

Modelling and analyzing the epidemic of human infections with the avian influenza A(H7N9) virus in 2017 in China

In 2013, in mainland China, a novel avian influenza A(H7N9) virus began to infect humans, followed by the annual outbreaks, and had aroused severe fatality in the infected humans. After introducing the statistical characteristics including the geographical distributions of the outbreaks, a SEV‐SIRS eco‐epidemiological model is established and analyzed. In this model, the factor of virus in environment is incorporated into the model as a class; the vaccine measure in poultry is taken into account in purpose of assessing its control effect in 2017 in China; the nonmonotonic contact function is adopted to characterize the psychosocial effect. The stability of disease‐free equilibrium point (DFE) is obtained by the threshold theory; the stability of the endemic equilibrium point is gotten by the Bendixson criterion based on the geometric approach. Sensitivity analyses of system parameters indicate that the measure of vaccination in poultry can play its role but only when the vaccine rate is more than 98% can the disease control effect be effectively exerted, and the virus in environment is an extremely sensitive factor in the disease transmission and the epidemic control.