The Exit Time and the Dividend Value Function for One-Dimensional Diffusion Processes

We investigate the exit times from an interval for a general one-dimensional time-homogeneous diffusion process and their applications to the dividend problem in risk theory. Specifically, we first use Dynkin’s formula to derive the ordinary differential equations satisfied by the Laplace transform of the exit times. Then, as some examples, we solve the closed-form expression of the Laplace transform of the exit times for several popular diffusions, which are commonly used in modelling of finance and insurance market. Most interestingly, as the applications of the exit times, we create the connect between the dividend value function and the Laplace transform of the exit times. Both the barrier and threshold dividend value function are clearly expressed in terms of the Laplace transform of the exit times

Parameter estimation algorithm for multivariable controlled autoregressive autoregressive moving average systems

This paper investigates parameter estimation problems for multivariable controlled autoregressive autoregressive moving average (M-CARARMA) systems. In order to improve the performance of the standard multivariable generalized extended stochastic gradient (M-GESG) algorithm, we derive a partially coupled generalized extended stochastic gradient algorithm by using the auxiliary model. In particular, we divide the identification model into several subsystems based on the hierarchical identification principle and estimate the parameters using the coupled relationship between these subsystems. The simulation results show that the new algorithm can give more accurate parameter estimates of the M-CARARMA system than the M-GESG algorithm

Highly computationally efficient state filter based on the delta operator

The Kalman filter is not suitable for the state estimation of linear systems with multistate delays, and the extended state vector Kalman filtering algorithm results in heavy computational burden because of the large dimension of the state estimation covariance matrix. Thus, in this paper, we develop a novel state estimation algorithm for enhancing the computational efficiency based on the delta operator. The computation analysis and the simulation example show the performance of the proposed algorithm