Journal of Advanced Statistics

10

Authors: Xinfeng Li, Hao Deng

To better supervise the risk of financial investment market, the Conditional Value At Risk (CVaR) investment portfolio optimization model of under single period investment is discussed and its expansion form is explained. The empirical simulation of Mean - CVaR model is carried out with historical simulation method, and the influence of confidence level and transaction cost on the effective frontier of the optimization model is mainly studied. The results show that the effective frontier of the Mean - CVaR model will move to the right as the confidence level increases and will also move to the lower right as the transaction cost increases. In addition, the empirical simulation part also confirms the rationality of the mean model and summarizes the relationship between -CVaR and - Value At Risk (VaR) and the characteristics of their respective effective frontier curves. It can be concluded that the Mean - CVaR model has a good effect on the risk supervision of financial investment market.

13

Authors: Qiqing Yu and Qinggang Diao

The semi-parametric estimation under the proportional hazards (PH) model with a linearly time-dependent covariates and with interval-censored data has not been investigated before. The partial likelihood approach does not work and one has to use the generalized likelihood function (GLF). There is a challenge in this problem. The GLF must be in the form of the baseline hazard function, rather than the baseline survival function as in the PH model with time-independent covariates, and a feasible way to specify the hazard function is a piece-wise constant function. However, several naive ways do not yield a consistent estimator. We propose proper modifications of the GLF. Simulation results suggest that our method works. The generalization to other types of time-dependent covariates is also discussed.