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Stochastic Finance

- Nicolas Privault
- Mathematics
- 20 December 2013

Introduction Assets, Portfolios and Arbitrage Definitions and Formalism Portfolio Allocation and Short-Selling Arbitrage Risk-Neutral Measures Hedging of Contingent Claims Market Completeness Example… Expand

Stochastic Analysis in Discrete and Continuous Settings: With Normal Martingales

- Nicolas Privault
- Mathematics
- 24 July 2009

The Discrete Time Case.- Continuous Time Normal Martingales.- Gradient and Divergence Operators.- Annihilation and Creation Operators.- Analysis on the Wiener Space.- Analysis on the Poisson Space.-… Expand

Stochastic analysis of Bernoulli processes

- Nicolas Privault
- Mathematics
- 18 September 2008

These notes survey some aspects of discrete-time chaotic calculus
and its applications, based on the chaos representation property
for i.i.d. sequences of random variables.
The topics covered… Expand

White noise generalizations of the Clark-Haussmann-Ocone theorem with application to mathematical finance

- K. Aase, B. Øksendal, Nicolas Privault, J. Ubøe
- MathematicsFinance Stochastics
- 17 November 2000

TLDR

Understanding Markov Chains: Examples and Applications

- Nicolas Privault
- Mathematics
- 7 August 2013

Introduction 1 Probability Background 1.1 Probability Spaces and Events 1.2 Probability Measures 1.3 Conditional Probabilities and Independence 1.4 Random Variables 1.5 Probability Distributions 1.6… Expand

Determinantal Point Processes

- L. Decreusefond, I. Flint, Nicolas Privault, G. Torrisi
- Mathematics
- 2016

In this survey we review two topics concerning determinantal (or fermion) point processes. First, we provide the construction of diffusion processes on the space of configurations whose invariant… Expand

Computations of Greeks in a market with jumps via the Malliavin calculus

- Youssef El-Khatib, Nicolas Privault
- MathematicsFinance Stochastics
- 1 May 2004

TLDR

Concentration and deviation inequalities in infinite dimensions via covariance representations

- C. Houdré, Nicolas Privault
- Mathematics
- 1 December 2002

Concentration and deviation inequalities are obtained for functionals on Wiener space, Poisson space or more generally for normal martingales and binomial processes. The method used here is based on… Expand

Convex concentration inequalities and forward-backward stochastic calculus

- T. Klein, Yutao Ma, Nicolas Privault
- Mathematics
- 7 July 2006

Given $(M_t)_{t\in \mathbb{R}_+}$ and $(M^*_t)_{t\in \mathbb{R}_+}$ respectively a forward and a backward martingale with jumps and continuous parts, we prove that $E[\phi (M_t+M^*_t)]$ is… Expand

An extension of stochastic calculus to certain non-Markovian processes

- Nicolas Privault
- Mathematics
- 1997

By time changes of Lévy processes we construct two operators on Fock space whose sum is a second quantized operator, and that complement the annihilation and creation operators whose probabilistic… Expand

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