This paper considers the problem of a capital-limited investor with log utility who has the opportunity to invest in a security that follows a parametric price process. While the investor knows the form of the process, the exact parameter values are not known and must be inferred by observing the evolution of the security's price over time. The approach that will be described is applicable to a...

Ornstein-Uhlenbeck models are continuous-time processes which have broad applications in finance as, e.g., volatility processes in stochastic volatility models or spread models in spread options and pairs trading. The paper presents a least squares estimator for the model parameter in a multivariate Ornstein-Uhlenbeck model driven by a multivariate regularly varying Lévy process with infinite v...

We analyze in this work the effect of the iterated application of the linear operator that maps a Wiener process onto an OrnsteinUhlenbeck process. The processes obtained after p iterations are called Ornstein-Uhlenbeck processes of order p (denoted OU(p)). Technically our composition of operators is easy to manipulate and its parameters can be computed efficiently because, as we show, in most ...

The first-passage time of a Markov process to a moving barrier is considered as a first-exit time for a vector whose components include the process and the barrier. Thus when the barrier is itself a solution of a differential equation, the theory of first-exit times for multidimensional processes may be used to obtain differential equations for the moments and density of the first-passage time ...

In the paper we consider problem of estimating parameters entering drift a fractional Ornstein-Uhlenbeck type process in non-ergodic case, when underlying stochastic integral is ...

We derive a new coupling of the running maximum of an Ornstein–Uhlenbeck process and the running maximum of an explicit i.i.d. sequence. We use this coupling to verify a conjecture of Darling and Erdős (1956).