Lewis and Mordecki have computed the Wiener–Hopf factorization of a Lévy process whose restriction of the Lévy measure on ]0,+∞[ has a rational Laplace transform. This allowed them to compute the distribution of (Xt,inf0≤s≤tXs). For the same class of Lévy processes, we compute the...

In Kuznetsov et al. (2011) a new Monte Carlo simulation technique was introduced for a large family of Lévy processes that is based on the Wiener–Hopf decomposition. We pursue this idea further by combining their technique with the recently introduced multilevel Monte Carlo methodology....

We introduce a model for stock prices consisting of a fundamental price process and a news impact curve, which allows for either overreaction, underreaction, or correct response to changes of the fundamental value. We further develop statistics based on OHLC data, which separately measure upside...

Given a process with independent increments X (not necessarily a martingale) and a large class of square integrable r.v. H = f(X T ), f being the Fourier transform of a finite measure μ, we provide a direct expression for Kunita-Watanabe and Föllmer-Schweizer decompositions of H. The...

We study a continuous-time problem of public good contribution under uncertainty for an economy with a finite number of agents. Each agent aims to maximize his expected utility allocating his initial wealth over a given time period between private consumption and repeated but irreversible...

Motivated by the recent results of Nualart and Xu (2013) concerning limits laws for occupation times of one dimensional symmetric stable processes, this paper proves a decomposition for functionals of one dimensional symmetric Lévy processes under certain conditions on the characteristic...

The most common approach for default dependence modelling is at present copula functions. Within this framework, the paper examines factor copulas, which are the industry standard, together with their latest development, namely the incorporation of sudden jumps to default instead of a pure...

This short communication considers a tandem queue fed by Lévy input. The main result concerns expressions for the Laplace transform of the transient workload in the downstream queue, under the condition that the system starts off empty. This expression greatly simplifies if the driving Lévy...

The payoff of many credit derivatives depends on the level of credit spreads. In particular, the payoff of credit derivatives with a leverage component is sensitive to jumps in the underlying credit spreads. In the framework of first passage time models we extend the model introduced in...

We consider a heat kernel approach for the development of stochastic pricing kernels. The kernels are constructed by positive propagators, which are driven by time-inhomogeneous Markov processes. We multiply such a propagator with a positive, time-dependent and decreasing weight function, and...