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Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations

- B. Bouchard, N. Touzi
- Mathematics
- 1 June 2004

Applications of Malliavin calculus to Monte Carlo methods in finance

- E. Fournié, J. Lasry, Jérôme Lebuchoux, P. Lions, N. Touzi
- Economics, MathematicsFinance Stochastics
- 1999

TLDR

Law Invariant Risk Measures Have the Fatou Property

- E. Jouini, W. Schachermayer, N. Touzi
- Mathematics
- 1 May 2005

S. Kusuoka [K 01, Theorem 4] gave an interesting dual characterizationof law invariant coherent risk measures, satisfying the Fatou property.The latter property was introduced by F. Delbaen [D 02].… Expand

Weak Dynamic Programming Principle for Viscosity Solutions

- B. Bouchard, N. Touzi
- MathematicsSIAM J. Control. Optim.
- 1 May 2011

We prove a weak version of the dynamic programming principle for standard stochastic control problems and mixed control-stopping problems, which avoids the technical difficulties related to the… Expand

Wellposedness of second order backward SDEs

- H. Soner, N. Touzi, Jianfeng Zhang
- Mathematics
- 31 March 2010

We provide an existence and uniqueness theory for an extension of backward SDEs to the second order. While standard Backward SDEs are naturally connected to semilinear PDEs, our second order… Expand

Optimal Stochastic Control, Stochastic Target Problems, and Backward SDE

- N. Touzi
- Mathematics
- 27 September 2012

Preface.- 1. Conditional Expectation and Linear Parabolic PDEs.- 2. Stochastic Control and Dynamic Programming.- 3. Optimal Stopping and Dynamic Programming.- 4. Solving Control Problems by… Expand

OPTIMAL MULTIPLE STOPPING AND VALUATION OF SWING OPTIONS

- R. Carmona, N. Touzi
- Mathematics
- 12 March 2008

The connection between optimal stopping of random systems and the theory of the Snell envelop is well understood, and its application to the pricing of American contingent claims is well known.… Expand

Contingent Claims and Market Completeness in a Stochastic Volatility Model

In an incomplete market framework, contingent claims are of particular interest since they improve the market efficiency. This paper addresses the problem of market completeness when trading in… Expand

OPTIMAL RISK SHARING FOR LAW INVARIANT MONETARY UTILITY FUNCTIONS

- E. Jouini, W. Schachermayer, N. Touzi
- Economics
- 12 March 2008

We consider the problem of optimal risk sharing of some given total risk between two economic agents characterized by law‐invariant monetary utility functions or equivalently, law‐invariant risk… Expand

Option Hedging And Implied Volatilities In A Stochastic Volatility Model

- É. Renault, N. Touzi
- Economics
- 1 July 1996

In the stochastic volatility framework of Hull and White (1987), we characterize the so-called Black and Scholes implied volatility as a function of two arguments the ratio of the strike to the… Expand

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