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A MongeAmpère type fully nonlinear equation on Hermitian manifolds
A fully nonlinear PDE problem from pricing CDS with counterparty risk
1.  Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556 
2.  Department of Mathematics, Tongji University, Shanghai 200092, China, China, China 
References:
[1] 
F. Black and J. Cox, Valuing corporate securities: Some effects of bond indenture provisions, Journal of Finance, 31 (1976), 351367. doi: 10.1111/j.15406261.1976.tb01891.x. 
[2] 
T. Bielecki and M. Rutkowski, "Credit Risk: Modeling, Valuation and Hedging," Springer Finance, SpringerVerlag, Berlin, 2002. 
[3] 
S. Crepey, M. Jeanblanc and B. Zargari, Counterparty risk on a CDS in a Markov Chain Copula model with joint defaults, working paper, 2009. 
[4] 
J. Cox, J. Ingersoll and S. Ross, A Theory of the term structure of interest rates, Econometrica, 53 (1985), 385407. doi: 10.2307/1911242. 
[5] 
D. Duffie and K. J. Singleton, Modeling term structures of defaultable bonds, Review of Financial Studies, 12 (1999), 687720. doi: 10.1093/rfs/12.4.687. 
[6] 
B. Øksendal, "Stochastic Differential Equations. An Introduction with Applications," fifth edition, Universitext, SpringerVerlag, Berlin, 1998. 
[7] 
A. Friedman, "Variational Principles and Free Boundary Problems," Second edition, Robert E. Krieger Publishing Co., Inc., Malabar, FL, 1988. 
[8] 
D. Lando, On Cox processes and credit risky securities, Review of Derivatives Research, 2 (1998), 99120. 
[9] 
F. Longstaff and E. Schwartz, A simple approach to valuing risky fixed and floating rate debt, Journal of Finance, 50 (1995), 789819. doi: 10.2307/2329288. 
[10] 
R. Merton, On the valuing of corporate debt: The risk structure of interest rates, Journal of Finance, 29 (1974), 449470. doi: 10.1111/j.15406261.1974.tb03058.x. 
show all references
References:
[1] 
F. Black and J. Cox, Valuing corporate securities: Some effects of bond indenture provisions, Journal of Finance, 31 (1976), 351367. doi: 10.1111/j.15406261.1976.tb01891.x. 
[2] 
T. Bielecki and M. Rutkowski, "Credit Risk: Modeling, Valuation and Hedging," Springer Finance, SpringerVerlag, Berlin, 2002. 
[3] 
S. Crepey, M. Jeanblanc and B. Zargari, Counterparty risk on a CDS in a Markov Chain Copula model with joint defaults, working paper, 2009. 
[4] 
J. Cox, J. Ingersoll and S. Ross, A Theory of the term structure of interest rates, Econometrica, 53 (1985), 385407. doi: 10.2307/1911242. 
[5] 
D. Duffie and K. J. Singleton, Modeling term structures of defaultable bonds, Review of Financial Studies, 12 (1999), 687720. doi: 10.1093/rfs/12.4.687. 
[6] 
B. Øksendal, "Stochastic Differential Equations. An Introduction with Applications," fifth edition, Universitext, SpringerVerlag, Berlin, 1998. 
[7] 
A. Friedman, "Variational Principles and Free Boundary Problems," Second edition, Robert E. Krieger Publishing Co., Inc., Malabar, FL, 1988. 
[8] 
D. Lando, On Cox processes and credit risky securities, Review of Derivatives Research, 2 (1998), 99120. 
[9] 
F. Longstaff and E. Schwartz, A simple approach to valuing risky fixed and floating rate debt, Journal of Finance, 50 (1995), 789819. doi: 10.2307/2329288. 
[10] 
R. Merton, On the valuing of corporate debt: The risk structure of interest rates, Journal of Finance, 29 (1974), 449470. doi: 10.1111/j.15406261.1974.tb03058.x. 
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