In this paper we study upper bounds for the density of solution of stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/3. We show that under some geometric conditions, in the regular case H > 1/2, the density of the solution satisfy the log-Sobolev inequality, the Gaussian concentration inequality and admits an upper Gaussian bound. In the rough c...

In this paper we study upper bounds for the density of solution to stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/3. We show that under some geometric conditions, in the regular case H > 1/2, the density of the solution satisfies the log-Sobolev inequality, the Gaussian concentration inequality and admits an upper Gaussian bound. In the rough...

Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when foraging in resource-poor environments. Yet, empirical studies reveal animals moving in a Brownian fa...

We use Malliavin calculus and the Clark-Ocone formula to derive the hedging strategy of an arithmetic Asian Call option in general terms. Furthermore we derive an expression for the density of the integral over time of a geometric Brownian motion, which allows us to express hedging strategy and price of the Asian option as an analytic, that is closed form, expression. Numerical computations whi...

We consider a renewal jump-diffusion process, more specifically a renewal insurance risk model with investments in a stock whose price is modeled by a geometric Brownian motion. Using Laplace transforms and regular variation theory, we introduce a transparent and unifying analytic method for investigating the asymptotic behavior of ruin probabilities and related quantities, in models with light...

Strongly inspired by the result due to Carr-Ewald-Xiao that the arithmetic average of geometric Brownian motion is an increasing process in the convex order, we extend this result to integrals of Lévy processes and Gaussian processes. Our method consists in finding an appropriate sheet associated to the original Lévy or Gaussian process, from which the one-dimensional marginals of the integrals...

Option pricing is mainly based on ideal market conditions which are well represented by the Geometric Brownian Motion (GBM) as market model. We study the effect of non-ideal market conditions on the price of the option. We focus our attention on two crucial aspects appearing in real markets: The influence of heavy tails and the effect of colored noise. We will see that both effects have opposit...

In this research various nonlinear fluid models have been introduced and the balloon movement in the porous arteries, including third-order non-Newtonian fluid, is described under the influence of the magnetic field. In order to solve the nonlinear equations governing the desired artery, an analytical method of approximation collocation and least squares are proposed. The effect of various para...

We introduce a simple model for the pricing of European style options when the underlying dividend process is given by a geometric Brownian motion with Markov-modulated coefficients. It turns out that the corresponding stock process is characterized by both stochastic coefficients and jumps. Transform methods are used to recover option prices. The model is calibrated to market data and the resu...