In this article, we study a double barrier version of the standard Parisian options. We give closed formulas for the Laplace transforms of their prices with respect to the maturity time. We explain how to invert them numerically and prove a result on the accuracy of the numerical inversion when...

In this paper, we are interested in the almost sure convergence of randomly truncated stochastic algorithms. In their pioneering work Chen and Zhu [Chen, H., Zhu, Y., 1986. Stochastic Approximation Procedure with Randomly Varying Truncations. In: Scientia Sinica Series.] required that the family...

This paper focuses on an extension of the limit order book (LOB) model with general shape introduced by Alfonsi, Fruth and Schied ((2010). Optimal execution strategies in limit order books with general shape functions. <italic>Quantitative Finance</italic>, <italic>10</italic>(2), 143-157). Here, the additional feature allows a...

We study the convergence of a drift implicit scheme for one-dimensional SDEs that was considered by Alfonsi (2005) for the Cox–Ingersoll–Ross (CIR) process. Under general conditions, we obtain a strong convergence of order 1. In the CIR case, Dereich et al. (2012) have shown recently a...

In this paper, we investigate the generalization of the Call-Put duality equality obtained in Alfonsi and Jourdain (preprint, 2006, available at ) for perpetual American options when the Call-Put payoff (y - x)+ is replaced by ϕ(x,y). It turns out that the duality still holds under monotonicity...

We introduce the two-dimensional shifted square-root diffusion (SSRD) model for interest-rate and credit derivatives with (positive) stochastic intensity. The SSRD is the unique explicit diffusion model allowing an automatic and separated calibration of the term structure of interest rates and...

We introduce a mean-reverting SDE whose solution is naturally defined on the space of correlation matrices. This SDE can be seen as an extension of the well-known Wright–Fisher diffusion. We provide conditions that ensure weak and strong uniqueness of the SDE, and describe its ergodic limit....