We work under a geometric Lévy market model: the stock price process is modelled by a SDE driven by a general Lévy process (taking into account jumps). Except for the geometric Brownian model and the geometric Poissonian model, the above described general geometric Lévy market models are incomplete models and there are many equivalent martingale measures. In this paper we suggest to enlarge the...

We generalize the notion of brownian bridge. More precisely, we study a standard brownian motion for which a certain functional is conditioned to follow a given law. Such processes appear as weak solutions of stochastic differential equations which we call conditioned stochastic differential equations. The link with the theory of initial enlargement of filtration is made and after a general pre...

We give a probabilistic representation of a one-dimensional diffusion, equation where the solution is discontinuous at 0 with a jump proportional to its flux. This kind of interface condition is usually seen as a semi-permeable barrier. For this, we use a process called here the snapping out Brownian motion, whose properties are studied. As this construction is motivated by applications, for ex...

We consider a problem of an optimal consumption strategy on the infinite time horizon when the short-rate is a diffusion process. General existence and uniqueness theorem is illustrated by the Vasicek and so-called invariant interval models. We show also that when the short-rate dynamics is given by a Brownian motion or a geometric Brownian motion, then the value function is infinite.

The CFD simulation has been undertaken concerning natural convection heat transfer of a nanofluid in vertical square enclosure, whose dimension, width height length (mm), is 40 40 90, respectively. The nanofluid used in the present study is -water with various volumetric fractions of the alumina nanoparticles ranging from 0-3%. The Rayleigh number is . Fluent v6.3 is used to simulate nanofluid ...

We obtain the Laplace transform and integrability properties of the integral over R+ of the call quantity associated with geometric Brownian motion with negative drift, thus adding a new element to the list of already studied Brownian perpetuities.

Risk management is an important issue when there is a catastrophic event that affects asset price in the market such as a sub-prime financial crisis or other financial crisis. By adding a jump term in the geometric Brownian motion, the jump diffusion model can be used to describe abnormal changes in asset prices when there is a serious event in the market. In this paper, we propose an importanc...

In this paper we explicitly solve a non-linear filtering problem with mixed observations, modelled by a Brownian motion and a generalized Cox process, whose jump intensity is given in terms of a Lévy measure. Motivated by empirical observations of R. Cont and P. Tankov we propose a model for financial assets, which captures the phenomenon of time-inhomogeneity of the jump size density. We apply...

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory