Volume 40, Issue 3-4

In this paper, we explore the idea of grouping under the massive data framework, to propose a median-of-means non-parametric type estimator for the Proportional Hazard Transform (PHT), which has been widely used in finance and insurance. Under certain conditions on the growth rate of subgroups, the consistency and asymptotic normality of the proposed estimators are investigated. Furthermore, we construct a new method to test PHT based on the empirical likelihood method for the median in order to avoid any prior estimate of the variance structure for the proposed estimator, as it is difficult to estimate and often causes much inaccuracy. Numerical simulations and real-data analysis are designed to show the present estimator’s performance. The results confirm that the new put-forward estimator is quite robust with respect to outliers.

In this paper, we study the analytical properties of the true solution to the generalised delay Ait-Sahalia-type interest rate model with Poisson-driven jumps. Since this model does not have a closed-form solution, we employ several new truncated Euler-Maruyama (EM) techniques to investigate the finite-time strong convergence theory of the numerical solution under the local Lipschitz condition plus the Khasminskii-type condition. We justify the strong convergence result for Monte Carlo calibration and valuation of some debt and derivative instruments.