We present a construction of a family of continuous-time ARMA processes based on p iterations of the linear operator that maps a Lévy process onto an Ornstein-Uhlenbeck process. The construction resembles the procedure to build an AR(p) from an AR(1). We show that this family is in fact a subfamily of the well-known CARMA(p,q) processes, with several interesting advantages, including a smaller ...

In this paper, we give the Laplace transform of the first hitting times to boundary and obtain its expectation on the reflected Ornstein-Uhlenbeck process with two-sided barriers. Finally,a comparison theorem is derived. Mathematics Subject Classification: 60H10

The log-likelihood of a nonhomogeneous Branching Diffusion Process under several conditions assuring existence and uniqueness of the diffusion part and nonexplosion of the branching process. Expressions for different Fisher information measures are provided. Using the semimartingale structure of the process and its local characteristics, a Girsanov-type result is applied. Finally, an Ornstein-U...

We consider the problem of the optimal trading strategy in the presence of linear costs, and with a strict cap on the allowed position in the market. Using Bellman’s backward recursion method, we show that the optimal strategy is to switch between the maximum allowed long position and the maximum allowed short position, whenever the predictor exceeds a threshold value, for which we establish an...

We show how to write the solution to the generalized drift Skorokhod problem in onedimension in terms of the supremum of the solution of an unrestricted integral equation (that is, an integral equation with no boundaries). As an application of our result, we equate the transient distribution of a reflected Ornstein-Uhlenbeck (O-U) process to the first hitting time distribution of an O-U process...