The story of modelling financial markets with stochastic processes began in 1900 with the
study of Bachelier (1900). He modelled stocks as a Brownian motion with drift. However, the …

We present a non-parametric method for calibrating jump-diffusion models to a set of
observed option prices. We show that the usual formulations of the inverse problem via …

In this paper we show the existence and uniqueness of a solution for backward stochastic
differential equations driven by a Lévy process with moments of all orders. The results are …

The risk‐neutral process is modeled by a four parameter self‐similar process of independent
increments with a self‐decomposable law for its unit time distribution. Six different processes …

This volume concentrates on how to construct a Markov process by starting with a suitable
pseudo-differential operator. Feller processes, Hunt processes associated with Lp-sub …

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These lectures notes aim at introducing L\'{e} vy processes in an informal and intuitive way,
accessible to non-specialists in the field. In the first part, we focus on the theory of L\'{e} vy …

This is a comprehensive introduction to the brand new theory of conic finance, also referred
to as the two-price theory, which determines bid and ask prices in a consistent and …

Models which hypothesize that returns are pure jump processes with independent
increments have been shown to be capable of capturing the observed variation of market …

This book is an introductory guide to using Lévy processes for credit risk modelling. It covers
all types of credit derivatives: from the single name vanillas such as Credit Default Swaps …