The standard GLM and GAM frequency-severity models assume independence between the claim frequency and severity. To overcome restrictions of linear or additive forms and to relax the independence assumption, we develop a data-driven dependent frequency-severity model, where we combine a stochastic gradient boosting algorithm and a profile likelihood approach to estimate parameters for both of the claim frequency and average claim severity distributions, and where we introduce the dependence between the claim frequency and severity by treating the claim frequency as a predictor in the regression model for the average claim severity. The model can flexibly capture the nonlinear relation between the claim frequency (severity) and predictors and complex interactions among predictors and can fully capture the nonlinear dependence between the claim frequency and severity. A simulation study shows excellent prediction performance of our model. Then, we demonstrate the application of our model with a French auto insurance claim data. The results show that our model is superior to other state-of-the-art models.

The aim of this paper is to develop a mean-variance model for portfolio optimization considering the background risk, liquidity and transaction cost based on uncertainty theory. In portfolio selection problem, returns of securities and assets liquidity are assumed as uncertain variables because of incidents or lacking of historical data, which are common in economic and social environment. We provide crisp forms of the model and a hybrid intelligent algorithm to solve it. Under a mean-variance framework, we analyze the portfolio frontier characteristic considering independently additive background risk. In addition, we discuss some effects of background risk and liquidity constraint on the portfolio selection. Finally, we demonstrate the proposed models by numerical simulations.

In the context of the aging population, the debt risk and solvency situation of China’s pension plan are of major concern for government and individuals. The aim of this paper is to project public pension liabilities and evaluate the solvency sustainability of China’s pension reform during transition periods. By using cohort component and actuarial models, transition debt and solvency sustainability are projected under the existing policy scenario and several sets of hypothetical policy scenarios. We find that the transition liabilities will peak in 2035 and the pension plan will become unsustainable in 2048 under existing policies. In the proposed scenario, postponing retirement age helps to maintain pension plan sustainability until 2083, but this option can’t solve the financial distress in the long run. Further, the transition pension debt will double in the peak moment if the retirement age is postponed for five years, which would pose a risk to the liquidity of the fund. Moreover, an increase to invest return can only improve the baseline solvency in short term. Sustainable options should be designed as composite reform measures, including retirement and investment adjustment.

This paper discusses an uncertain portfolio selection problem with consideration of background risk and asset liquidity. In addition, the transaction costs are also considered. The security returns, background asset return, and asset liquidity are estimated by experienced experts instead of historical data. Regarding them as uncertain variables, a mean‐risk model with background risk, liquidity, and transaction costs is proposed for portfolio selection and the crisp forms of the model are provided when security returns obey different uncertainty distributions. Moreover, for better understanding of the impact of background risk and liquidity on portfolio selection, some important theorems are proved. Finally, numerical experiments are presented to illustrate the modeling idea.

In the uncertain environment of population and economy; the pension plan for urban employees in China is under threat from various types of financial risk. This paper mainly builds a comprehensive risk assessment system to evaluate the solvency sustainability of the urban employees’ pension plan of China. Specifically, we forecast annual accumulative net asset; actuarial balance; and potential support ratio for the next seventy years. To account for the impact of demographic uncertainty on long-term finances, stochastic simulations are used to estimate the probability distribution of relative risk indicators. Moreover, we integrate the Lee–Carter model into the population projection. According to the median projection, the public pension fund will have a gap in about 35 years; and the cash flow will be negative about 25 years later. Furthermore, under the existing policy, the burden of insured employees will increase rapidly. Delayed retirement could relieve the coming solvency risk, but it does not fundamentally resolve the solvency problem in the long run.