Fourier normal ordering (Unterberger, 2009) [34] is a new algorithm to construct explicit rough paths over arbitrary Hölder-continuous multidimensional paths. We apply in this article the Fourier normal ordering algorithm to the construction of an explicit rough path over multi-dimensional...

The numéraire portfolio in a financial market is the unique positive wealth process that makes all other nonnegative wealth processes, when deflated by it, supermartingales. The numéraire portfolio depends on market characteristics, which include: (a) the information flow available to...

We prove that a stationary max-infinitely divisible process is mixing (ergodic) iff its dependence function converges to 0 (is Cesàro summable to 0). These criteria are applied to some classes of max-infinitely divisible processes.

The class of coalescent processes with simultaneous multiple collisions ([Xi]-coalescents) without proper frequencies is considered. We study the asymptotic behavior of the external branch length, the total branch length and the number of mutations on the genealogical tree as the sample size n...

In this paper, we will study a class of backward stochastic differential equations (BSDEs for short), for which the generator (coefficient) g(t,y,z) is Lipschitz continuous with respect to y and uniformly continuous with respect to z. We establish several properties for such BSDEs, including...

Sample path Large Deviation Principles (LDP) of the Freidlin-Wentzell type are derived for a class of diffusions, which govern the price dynamics in common stochastic volatility models from Mathematical Finance. LDP are obtained by relaxing the non-degeneracy requirement on the diffusion matrix...

We consider backward stochastic differential equations with drivers of quadratic growth (qgBSDE). We prove several statements concerning path regularity and stochastic smoothness of the solution processes of the qgBSDE, in particular we prove an extension of Zhang's path regularity theorem to...

We study stochastic equations of non-negative processes with jumps. The existence and uniqueness of strong solutions are established under Lipschitz and non-Lipschitz conditions. Under suitable conditions, the comparison properties of solutions are proved. Those results are applied to construct...

We use the whole-plane Loewner equation to define a family of continuous LERW in finitely connected domains that are started from interior points. These continuous LERW satisfy conformal invariance, preserve some continuous local martingales, and are the scaling limits of the corresponding...

We consider the dividend payments of a self-financing firm in the stochastic Ramsey model. The firm invests in capital stock and its production technology is given by the Cobb-Douglas function. Our objective is to maximize the expected present value of future real dividends subject to a positive...