The Wiener-Hopf factorization of a complex function arises in a variety of fields in applied mathematics such as probability, finance, insurance, queuing theory, radio engineering and fluid mechanics. The factorization fully characterizes the distribution of functionals of a random walk or a...

The idea of this document is to provide the reader with an intuitive, yet rigorous and comprehensive introduction to the main tools in stochastic analysis required in Finance to understand the modern modelling, pricing and hedging techniques. The most important models (Brownian motion,...

The entry into force of the Solvency II regulatory regime is pushing insurance companies in engaging into market consistence evaluation of their balance sheet, including the financial options and guarantees embedded in life with-profit funds. The robustness of these valuations is crucial for...

We present a numerical scheme to calculate fluctuation identities for exponential L'evy processes in the continuous monitoring case. This includes the Spitzer identities for touching a single upper or lower barrier, and the more difficult case of the two-barriers exit problem. These identities...

This article presents lower and upper bounds on the prices of basket options for a general class of continuous-time financial models. The techniques we propose are applicable whenever the joint characteristic function of the vector of log-returns is known in closed-form. Moreover, the basket...

The aim of this paper is to shed new light on the concept of diversification showing that it is not necessarily related to the reduction of the volatility of a portfolio, as it is commonly perceived. We introduce a diversification index that exploits the decomposition of portfolio volatility...

In the present paper, we convert the usual <italic>n</italic>-step backward recursion that arises in option pricing into a set of independent integral equations by using a <italic>z</italic>-transform approach. In order to solve these equations, we consider different quadrature procedures that transform the integral equation...

We present methodologies to price discretely monitored Asian options when the underlying evolves according to a generic Levy process. For geometric Asian options we provide closed-form solutions in terms of the Fourier transform and we study in particular these formulas in the Levy-stable case....

We compute an analytical expression for the moment generating function of the joint random vector consisting of a spot price and its discretely monitored average for a large class of square-root price dynamics. This result, combined with the Fourier transform pricing method proposed by Carr and...