Related papers: Correlated time-changed L\'evy Processes

Carr and Wu (2004), henceforth CW, developed a framework that encompasses almost all of the continuous-time models proposed in the option pricing literature. Their framework hinges on the stopping time property of the time changes. By…

Recently Carr and Wu (2004, 2005) and also Huang and Wu (2004) show that most stochastic processes used in traditional option pricing models can be cast as special cases of time-changed L\'evy processes. In particular these are models which…

In this paper we analyse time change equations (TCEs) for L\'evy-type processes in detail. To this end we establish a connection between TCEs and classical one-dimensional initial value problems (IVPs) which are easier to handle. Properties…

In this paper continuous time random walk models approximating fractional space-time diffusion processes are studied. Stochastic processes associated with the considered equations represent time-changed processes, where the time-change…

This article is devoted to some time-changed stochastic models based on multivariate stable processes. The considered models have several advantages in comparison with classical time-changed Brownian motions - for instance, it turns out…

This article proposes and studies warped-linear models for time series classification. The proposed models are time-warp invariant analogues of linear models. Their construction is in line with time series averaging and extensions of…

In this paper we propose a general derivative pricing framework which employs decoupled time-changed (DTC) L\'evy processes to model the underlying asset of contingent claims. A DTC L\'evy process is a generalized time-changed L\'evy…

Partial observations of continuous time-series dynamics at arbitrary time stamps exist in many disciplines. Fitting this type of data using statistical models with continuous dynamics is not only promising at an intuitive level but also has…

In this paper, we consider a wide class of time-varying multivariate causal processes which nests many classic and new examples as special cases. We first prove the existence of a weakly dependent stationary approximation for our model…

Anomalous diffusions arise as scaling limits of continuous-time random walks (CTRWs) whose innovation times are distributed according to a power law. The impact of a non-exponential waiting time does not vanish with time and leads to…

Uncertainty quantification of predictive models is crucial in decision-making problems. Conformal prediction is a general and theoretically sound answer. However, it requires exchangeable data, excluding time series. While recent works…

We introduce a general theory on stationary approximations for locally stationary continuous-time processes. Based on the stationary approximation, we use $\theta$-weak dependence to establish laws of large numbers and central limit type…

Cai, Song and Kou (2015) [Cai, N., Y. Song, S. Kou (2015) A general framework for pricing Asian options under Markov processes. Oper. Res. 63(3): 540-554] made a breakthrough by proposing a general framework for pricing both discretely and…

DTW calculates the similarity or alignment between two signals, subject to temporal warping. However, its computational complexity grows exponentially with the number of time-series. Although there have been algorithms developed that are…

We introduce an algorithm for the pricing of finite expiry American options driven by L\'evy processes. The idea is to tweak Carr's `Canadisation' method, cf. Carr [9] (see also Bouchard et al [5]), in such a way that the adjusted algorithm…

In this paper we study coupled fully non-local equations, where a linear non-local operator jointly acts on the time and space variables. We establish existence and uniqueness of the solution. A maximum principle is proved and used to…

This paper reviews compact continuous-time formulations for the multi-mode resource-constrained project scheduling problem. Specifically, we first point out a serious flaw in an existing start-end-event-based formulation owing to…

Many records in environmental sciences exhibit asymmetric trajectories and there is a need for simple and tractable models which can reproduce such features. In this paper we explore an approach based on applying both a time change and a…

Conformal prediction offers a practical framework for distribution-free uncertainty quantification, providing finite-sample coverage guarantees under relatively mild assumptions on data exchangeability. However, these assumptions cease to…

This paper develops power series expansions of a general class of moment functions, including transition densities and option prices, of continuous-time Markov processes, including jump--diffusions. The proposed expansions extend the ones…