Arnsdorf and I. Halperin. BSLP: Markovian Bivariate Spread-Loss Model for Portfolio Credit Derivatives, J. Comput. Finance, vol.12, issue.2, pp.77-107, 2008. ,
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 1964. ,
Applying series expansion to the inverse beta distribution to find percentiles of the F-distribution, ACM Transactions on Mathematical Software, vol.19, issue.4, pp.474-480, 1993. ,
DOI : 10.1145/168173.168387
All your hedges in one basket, Risk November, vol.16, issue.11, pp.67-72, 2003. ,
On irregular functionals of SDEs and the Euler scheme, Finance and Stochastics, vol.13, issue.3, pp.381-401, 2009. ,
Discrete-time approximation for continuously and discretely reflected BSDEs, Stochastic Processes and their Applications, vol.118, issue.12, pp.2269-2293, 2008. ,
DOI : 10.1016/j.spa.2007.12.007
Up and down credit risk Working paper, 2008. ,
L p solutions of backward stochastic differential equations, Stochastic Processes and their Applications, pp.109-129, 2003. ,
Discrete-time approximation of decoupled Forward???Backward SDE with jumps, Stochastic Processes and their Applications, pp.53-75, 2008. ,
DOI : 10.1016/j.spa.2007.03.010
URL : https://hal.archives-ouvertes.fr/hal-00362300
On the Malliavin approach to Monte Carlo approximation of conditional expectations, Finance and Stochastics, vol.8, issue.1, pp.45-71, 2004. ,
DOI : 10.1007/s00780-003-0109-0
URL : https://hal.archives-ouvertes.fr/hal-00101982
BSDE with quadratic growth and unbounded terminal value, Probab. Theory Relat. Fields, vol.136, issue.4, pp.604-618, 2006. ,
An introduction to simulation of risk processes. Research note, 2004. ,
Conjugate convex functions in optimal stochastic control, J. Math. Anal. Appl, vol.44, pp.383-404, 1973. ,
One-dimensional backward stochastic differential equations whose coefficient is monotonic in y and non-Lipschitz in z, Bernoulli, vol.13, issue.1, pp.80-91, 2007. ,
Strong approximations of BSDEs in a domain, Bernoulli, vol.15, issue.4, 2008. ,
DOI : 10.3150/08-BEJ181
URL : https://hal.archives-ouvertes.fr/hal-00446316
Error analysis of the optimal quantization algorithm for obstacle problems, Stochastic Processes and their Applications, pp.1-40, 2003. ,
DOI : 10.1016/S0304-4149(03)00026-7
URL : https://hal.archives-ouvertes.fr/hal-00103987
The Pricing of Options and Corporate Liabilities, Journal of Political Economy, vol.81, issue.3, pp.637-654, 1973. ,
DOI : 10.1086/260062
Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations, Stochastic Processes and their Applications, pp.175-206, 2004. ,
DOI : 10.1016/j.spa.2004.01.001
URL : https://hal.archives-ouvertes.fr/hal-00103046
On the convergence of higher order hedging schemes, 2008. ,
Importance sampling and interacting particle systems for the estimation of Markovian credit portfolios loss distributions Available at http://grozny.maths.univ-evry.fr, 2009. ,
Interacting particle systems for the computation of rare credit portfolio losses, Finance and Stochastics, vol.14, issue.4, pp.613-633, 2009. ,
DOI : 10.1007/s00780-009-0098-8
A discrete-time approximation for doubly reflected BSDEs, Advances in Applied Probability, vol.41, issue.01, pp.101-130, 2009. ,
DOI : 10.1111/1467-9965.00022
Numerical methods for backward stochastic differential equations, In Numerical Methods in Finance, pp.232-244, 1997. ,
Recovering portfolio default intensities implied by CDO quotes, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00788571
Analyse du risque et couverture des tranches de CDO synthétiques, 2008. ,
Forward equations for portfolio credit derivatives Available on SSRN preprint server, 2008. ,
Credit Derivatives: CDOs and Structured Credit Products (Wiley Finance), 2005. ,
Stochastic Differential Utility, Econometrica, vol.60, issue.2, pp.353-394, 1992. ,
DOI : 10.2307/2951600
Financial Markets with Transaction Costs; Leland's Strategies and Arbitrage, 2008. ,
Non-Uniform Random Variate Generation, 1986. ,
Risk and Valuation of Collateralized Debt Obligations, Financial Analysts Journal, vol.57, issue.1, pp.41-59, 2001. ,
DOI : 10.2469/faj.v57.n1.2418
Time-Changed Birth Processes and Multi-Name Credit Derivatives, Operations Research, 2009. ,
Infectious defaults, Quantitative Finance, vol.1, issue.4, pp.382-387, 2001. ,
DOI : 10.1080/713665832
A forward???backward stochastic algorithm for quasi-linear PDEs, The Annals of Applied Probability, vol.16, issue.1, pp.140-184, 2006. ,
DOI : 10.1214/105051605000000674
URL : https://hal.archives-ouvertes.fr/hal-00005448
Numerical analysis of jump diffusion models: A partial differential equation approach ,
Finite difference methods in financial engineering. A partial differential equation approach. Wiley Finance Series, 2006. ,
Affine Point Processes and Portfolio Credit Risk, SIAM Journal on Financial Mathematics, vol.1, issue.1, 2009. ,
DOI : 10.1137/090771272
PRICING AND HEDGING OF PORTFOLIO CREDIT DERIVATIVES WITH INTERACTING DEFAULT INTENSITIES, International Journal of Theoretical and Applied Finance, vol.11, issue.06, pp.11611-634, 2008. ,
DOI : 10.1142/S0219024908004956
Applications of Malliavin calculus to Monte Carlo methods in finance, BIBLIOGRAPHY [Fri64] A. Friedman. Partial differential equations of parabolic type, pp.391-412, 1964. ,
Polynomial approximation of differential equations. Lecture Notes in Physics. New Series m: Monographs, 1992. ,
Quantitative approximation of certain stochastic integrals, Stoch. Stoch. Rep, vol.73, issue.3-4, pp.241-270, 2002. ,
On approximation of a class of stochastic integrals and interpolation, Stochastics and Stochastics Reports, vol.76, issue.4, pp.339-362, 2004. ,
DOI : 10.1080/10451120410001728445
Interpolation and approximation in <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>??</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>, Journal of Approximation Theory, vol.144, issue.2, pp.213-232, 2007. ,
DOI : 10.1016/j.jat.2006.06.001
The correlation-neutral measure for portfolio credit, 2007. ,
Portfolio credit risk: Top down versus bottom up approaches . Frontiers in Quantitative Finance: Credit Risk and Volatility Modeling, 2008. ,
Basket default swaps, CDOs and factor copulas, Journal of Risk, vol.7, issue.4, pp.103-122, 2005. ,
Numerical simulation of BSDEs using empirical regression methods: theory and practice Available on HAL preprint server, Proceedings of the Fifth Colloquium on BSDEs, 2005. ,
Error expansion for the discretization of backward stochastic differential equations, Stochastic Processes and their Applications, pp.803-829, 2007. ,
DOI : 10.1016/j.spa.2006.10.007
URL : https://hal.archives-ouvertes.fr/hal-00019463
Solving BSDE with Adaptive Control Variate, SIAM Journal on Numerical Analysis, vol.48, issue.1, 2009. ,
DOI : 10.1137/090755060
URL : https://hal.archives-ouvertes.fr/hal-00498268
Monte Carlo methods in financial Engineering. Applications of Mathematics 53, 2004. ,
Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations, Bernoulli, vol.12, issue.5, pp.889-916, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-00394976
A spectral Monte Carlo method for the Poisson equation, Monte Carlo Methods and Applications, vol.10, issue.3-4, pp.3-4275, 2004. ,
DOI : 10.1515/mcma.2004.10.3-4.275
URL : https://hal.archives-ouvertes.fr/hal-01479844
Sequential control variates for functionals of markov processes, SIAM Journal on Numerical Analysis, vol.43, issue.3, pp.1256-1275, 2005. ,
Sensitivity analysis using Itô-Malliavin calculus and martingales, and application to stochastic optimal control, SIAM Journal on control and optimization, vol.43, issue.5, pp.1676-1713, 2005. ,
L 2 -time regularity of BSDEs with irregular terminal functions, revision for Stochastic Processes and their Applications . Available on HAL preprint server, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00291768
Correlation expansions for CDO pricing, Journal of Banking & Finance, vol.31, issue.5, pp.1375-1398, 2007. ,
DOI : 10.1016/j.jbankfin.2006.10.018
Discrete time hedging errors for options with irregular payoffs, Finance and Stochastics, vol.5, issue.3, pp.357-367, 2001. ,
DOI : 10.1007/PL00013539
Weak convergence of error processes in discretizations of stochastic integrals and Besov spaces, Bernoulli, vol.15, issue.4, 2008. ,
DOI : 10.3150/09-BEJ197
Sequential Monte Carlo, Proc. Camb, pp.57-78, 1962. ,
A retrospective and prospective survey of the Monte Carlo method, SIAM Rev, vol.12, pp.1-63, 1970. ,
On the Starting and Stopping Problem: Application in Reversible Investments, Mathematics of Operations Research, vol.32, issue.1, pp.182-192, 2007. ,
DOI : 10.1287/moor.1060.0228
Zero-sum stochastic differential games and backward equations, Systems & Control Letters, vol.24, issue.4, pp.259-263, 1995. ,
DOI : 10.1016/0167-6911(94)00011-J
EVALUATING HEDGING ERRORS: AN ASYMPTOTIC APPROACH, Mathematical Finance, vol.80, issue.2, pp.309-343, 2005. ,
DOI : 10.1007/s004400050134
Martingales and stochastic integrals in the theory of continuous trading, Stochastic Processes and their Applications, pp.215-260, 1981. ,
DOI : 10.1016/0304-4149(81)90026-0
Climbing down from the top: Single name dynamics in credit top down models Working paper Available on arXiv preprint server. BIBLIOGRAPHY [Hul09] J.C. Hull. Options, futures, and other derivatives Valuation of a CDO and n th to default CDS without Monte-Carlo simulation, NJ The Journal of Derivatives, vol.12, issue.2, pp.8-23, 2004. ,
On continuous conditional Gaussian martingales and stable convergence in law Séminaire de probabilités XXXI, Azéma, J. Lect. Notes Math, vol.1655, pp.232-246, 1997. ,
Counterparty Risk and the Pricing of Defaultable Securities, Continuous Univariate Distributions, pp.1765-1799, 1995. ,
BSDEs and applications Indifference pricing: Theory and applications, Princeton Series in Financial Engineering, pp.267-320, 2009. ,
Stein's method and zero bias transformation for CDO tranche pricing, Finance and Stochastics, 2009. ,
Valuation and VaR computation for CDOs using Stein's method Applied quantitative finance, pp.161-189, 2009. ,
Robustness of the Black and Scholes Formula, Mathematical Finance, vol.8, issue.2, pp.93-126, 1998. ,
DOI : 10.1111/1467-9965.00047
Reflected solutions of backward SDE's, and related obstacle problems for PDE's, Ann. Probab, vol.25, issue.2, pp.702-737, 1997. ,
Backward stochastic differential equations and partial differential equations with quadratic growth, Ann. Probab, vol.28, issue.2, pp.558-602, 2000. ,
Reflected backward SDEs and American options Numerical methods in finance. Session at the Isaac Newton Institute, pp.215-231, 1995. ,
Backward stochastic differential equations in finance, Mathematical Finance, vol.7, issue.1, pp.1-71, 1997. ,
Brownian motion and stochastic calculus, 1991. ,
On Leland's strategy of option pricing with transactions costs, Finance and Stochastics, vol.1, issue.3, pp.239-250, 1997. ,
DOI : 10.1007/s007800050023
Option pricing and replication with transactions costs, Journal of Finance, vol.40, issue.5, pp.1283-1301, 1985. ,
Options pricing with transaction costs: an asymptotic approach, 1997. ,
Two-dimensional Markovian model for dynamics of aggregate credit loss, working paper, NumeriX, 2007. ,
Monte-Carlo Methods for the Transport and Diffusion Equations (Méthodes de Monte-Carlo pour les Equations de Transport et de Diffusion, Mathématiques et Applications, 1998. ,
An Empirical Analysis of the Pricing of Collateralized Debt Obligations, Mar78] W. Margrabe, pp.529-563177, 1978. ,
DOI : 10.1111/j.1540-6261.2008.01330.x
Propagation of convexity by Markovian and martingalian semigroups, Potential Anal, vol.10, issue.2, pp.133-175, 1999. ,
Genealogical particle analysis of rare events, The Annals of Applied Probability, vol.15, issue.4, pp.2496-2534, 2005. ,
DOI : 10.1214/105051605000000566
URL : https://hal.archives-ouvertes.fr/hal-00113982
Variance optimal hedging in the Black-Scholes model for a given number of transactions, 1999. ,
URL : https://hal.archives-ouvertes.fr/inria-00072895
Representation theorems for backward stochastic differential equations, The Annals of Applied Probability, vol.12, issue.4, pp.1390-1418, 2002. ,
DOI : 10.1214/aoap/1037125868
Malliavin calculus and related topics BIBLIOGRAPHY [Par98] E. Pardoux. Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order, Stochastic analysis and related topics, pp.79-127, 1996. ,
Limit theorem for Leland's strategy. The Annals of Applied Probability, pp.1099-1118, 2003. ,
Adapted solution of a backward stochastic differential equation, Systems & Control Letters, vol.14, issue.1, pp.55-61, 1990. ,
DOI : 10.1016/0167-6911(90)90082-6
Backward stochastic differential equations and quasilinear parabolic partial differential equations, Proc. IFIP Int. Conf., Charlotte/NC (USA) 1991, pp.200-217, 1992. ,
DOI : 10.1007/BFb0007334
Numerical Recipes in C, 1992. ,
La Gestion des Risques Financiers, Economica, 2004. ,
Limit distributions for the error in approximations of stochastic integrals, Ann. Probab, vol.8, pp.241-251, 1980. ,
Continuous martingales and Brownian motion, 1994. ,
Efficient solution of a partial integro-differential equation in finance, Applied Numerical Mathematics, vol.58, issue.11, pp.1687-1703, 2008. ,
DOI : 10.1016/j.apnum.2007.11.002
Multidimensional diffusion processes, 1979. ,
DOI : 10.1007/3-540-28999-2
Analysis of Error with Malliavin Calculus: Application to Hedging, Mathematical Finance, vol.32, issue.1, pp.201-214, 2003. ,
DOI : 10.1111/1467-9965.00014
Equations intégro-différentielles d'évolution : méthodes numériques et applications en finance, 2005. ,
Couverture approchée des options Européennes A numerical scheme for BSDEs, Ecole Nationale des Ponts et Chaussées The Annals of Applied Probability, vol.14, issue.1, pp.459-488, 1999. ,