Asset transaction prices sampled at high frequency are much staler than one might expect in the sense that they frequently lack new updates showing zero returns. In this paper, we propose a theoretical framework for formalizing this phenomenon. It hinges on the existence of a latent...

This paper deals with empirical processes of the type Cn(B) = n^(1/2) {µn(B) - P(Xn+1 in B | X1, . . . ,Xn)} , where (Xn) is a sequence of random variables and µn = (1/n)SUM(i=1,..,n) d(Xi) the empirical measure. Conditions for supB|Cn(B)| to converge stably (in particular, in distribution)...

We study a mixed hitting-time (MHT) model that specifies durations as the first time a Lévy process - a continuous-time process with stationary and independent increments - crosses a heterogeneous threshold. Such models are of substantial interest because they can be reduced from...

We study the relation between Lévy processes under nonlinear expectations, nonlinear semigroups and fully nonlinear PDEs. First, we establish a one-to-one relation between nonlinear Lévy processes and nonlinear Markovian convolution semigroups. Second, we provide a condition on a family of...

We derive a new equation for the optimal investment boundary of a general irreversible investment problem under exponential Lévy uncertainty. The problem is set as an infinite time-horizon, two-dimensional degenerate singular stochastic control problem. In line with the results recently...