Project Euclid

References

• Arvanitis, A. and Gregory, J. (2001). Credit: The Complete Guide to Pricing, Hedging and Risk Management. Risk Books, London.
• Becherer, D. (2001). Rational hedging and valuation with utility-based preferences. Ph.D. thesis, TU Berlin. Available at edocs.tu-berlin.de/diss/2001/becherer_dirk.htm.
• Becherer, D. (2004). Utility-indifference hedging and valuation via reaction–diffusion systems. Proc. Roy. Soc. London Ser. A 460 27–51.
  Mathematical Reviews (MathSciNet): MR2052255
  Zentralblatt MATH: 1087.91019
  Digital Object Identifier: doi:10.1098/rspa.2003.1234
  
• Bélanger, A., Shreve, S. and Wong, D. (2004). A general framework for pricing credit risk. Math. Finance 14 317–350.
  Mathematical Reviews (MathSciNet): MR2070167
  Digital Object Identifier: doi:10.1111/j.0960-1627.2004.t01-1-00193.x
  
• Bielecki, T. and Rutkowski, M. (2002). Credit Risk: Modelling, Valuation and Hedging. Springer, Berlin.
  Zentralblatt MATH: 0979.91050
  
• Blanchet-Scalliet, C. and Jeanblanc, M. (2004). Hazard rate for credit risk and hedging defaultable contingent claims. Finance and Stochastics 8 145–159.
  Zentralblatt MATH: 1052.91036
  Digital Object Identifier: doi:10.1007/s00780-003-0108-1
  
• Brémaud, P. (1981). Point Processes and Queues. Springer, Berlin.
• Davis, M. and Lischka, F. (2002). Convertible bonds with market risk and credit risk. In Applied Probability. Studies in Advanced Mathematics (D. Chan, Y.-K. Kwok, D. Yao and Q. Zhang, eds.) 45–58. Amer. Math. Soc., Providence, RI.
  Mathematical Reviews (MathSciNet): MR1909877
  Zentralblatt MATH: 1029.91033
  
• Davis, M. and Lo, V. (2001). Modelling default correlation in bond portfolios. In Mastering Risk 2. Applications (C. Alexander, ed.) 141–151. Financial Times/Prentice Hall, Englewood Cliffs, NJ.
• Di Masi, G., Kabanov, Y. and Runggaldier, W. (1994). Mean-variance hedging of options on stocks with Markov volatilities. Theory Probab. Appl. 39 172–182.
  Zentralblatt MATH: 0836.60075
  
• Duffie, D. and Epstein, L. (1992). Stochastic differential utility. Econometrica 60 353–394.
  Zentralblatt MATH: 0763.90005
  Digital Object Identifier: doi:10.2307/2951600
  
• Duffie, D., Schroder, M. and Skiadas, C. (1996). Recursive valuation of defaultable securities and the timing of resolution of uncertainty. Ann. Appl. Probab. 6 1075–1090.
  Zentralblatt MATH: 0868.90008
  Digital Object Identifier: doi:10.1214/aoap/1035463324
  Project Euclid: euclid.aoap/1035463324
  
• Föllmer, H. and Schweizer, M. (1991). Hedging of contingent claims under incomplete information. In Applied Stochastic Analysis. Stochastics Monographs 5 (M. H. A. Davis and R. J. Elliott, eds.) 389–414. Gordon and Breach, New York.
• Föllmer, H. and Sondermann, D. (1986). Hedging of non-redundant contingent claims. In Contributions to Mathematical Economics in Honor of Gerard Debreu (W. Hildenbrand and A. Mas-Colell, eds.) 205–223. North-Holland, Amsterdam.
  Zentralblatt MATH: 0663.90006
  
• Freidlin, M. (1985). Functional Integration and Partial Differential Equations. Princeton, New Jersey.
  Zentralblatt MATH: 0568.60057
  
• Friedman, A. (1975). Stochastic Differential Equations and Applications 1. Academic Press, New York.
  Zentralblatt MATH: 0323.60056
  
• Heath, D. and Schweizer, M. (2001). Martingales versus PDEs in finance: An equivalence result with examples. J. Appl. Probab. 37 947–957.
  Zentralblatt MATH: 0996.91069
  Digital Object Identifier: doi:10.1239/jap/1014843075
  Project Euclid: euclid.jap/1014843075
  
• Jacod, J. and Protter, P. (1982). Quelques remarques sur un nouveau type d'équations différentielles stochastiques. Séminaire de Probabilités XVI. Lecture Notes in Math. 920 447–458. Springer, Berlin.
• Jarrow, R. and Yu, F. (2001). Counterparty risk and the pricing of derivative securities. J. Finance 56 1765–1799.
• Jeanblanc, M. and Rutkowski, M. (2003). Modelling and hedging of credit risk. In Credit Derivatives: The Definitive Guide (J. Gregory, ed.) 385–416. Risk Books, London.
• Krylov, N. (1987). Nonlinear Elliptic and Parabolic Equations of the Second Order. Reidel Publishing and Kluver Academic Publishers, Dordrecht.
  Zentralblatt MATH: 0619.35004
  
• Kunita, H. (1984). Stochastic differential equations and stochastic flows of diffeomorphisms. École d'Été de Probabilités de Saint-Flour XII. Lecture Notes in Math. 1097 142–303. Springer, Berlin.
  Mathematical Reviews (MathSciNet): MR876080
  
• Kusuoka, S. (1999). A remark on default risk models. Advances in Mathematical Economics 1 69–82.
  Zentralblatt MATH: 0939.60023
  
• Lando, D. (1998). On Cox processes and credit risky securities. Review of Derivatives Research 2 99–120.
  Zentralblatt MATH: 1274.91459
  
• Madan, D. and Unal, H. (1998). Pricing the risk of default. Review of Derivatives Research 2 121–160.
  Zentralblatt MATH: 1274.91426
  
• Møller, T. (2001). Risk-minimizing hedging strategies for insurance payment processes. Finance and Stochastics 5 419–446.
• Møller, T. (2003). Indifference pricing of insurance contracts in a product space model. Finance and Stochastics 7 197–217.
• Pardoux, E. (1999). BSDEs, weak convergence and homogenization of semilinear PDEs. In Nonlinear Analysis, Differential Equations and Control (F. H. Clarke and R. J. Stern, eds.) 503–549. Kluwer Academic, Dordrecht.
  Zentralblatt MATH: 0959.60049
  
• Pazy, A. (1983). Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, Berlin.
  Zentralblatt MATH: 0516.47023
  
• Protter, P. (2004). Stochastic Integration and Differential Equations. Springer, Berlin.
  Mathematical Reviews (MathSciNet): MR2020294
  Zentralblatt MATH: 1041.60005
  
• Ramlau-Hansen, H. (1990). Thiele's differential equation as a tool in product development in life insurance. Scand. Actuar. J. 97–104.
  Zentralblatt MATH: 0746.62101
  Digital Object Identifier: doi:10.1080/03461238.1990.10413874
  
• Schönbucher, P. J. (2003). Credit Derivatives Pricing Models. Wiley, Chichester.
• Schweizer, M. (1991). Option hedging for semimartingales. Stochastic Process. Appl. 37 339–363.
  Zentralblatt MATH: 0735.90028
  Digital Object Identifier: doi:10.1016/0304-4149(91)90053-F
  
• Schweizer, M. (2001). A guided tour through quadratic hedging approaches. In Option Pricing, Interest Rates and Risk Management (E. Jouini, J. Cvitanić and M. Musiela, eds.) 538–574. Cambridge Univ. Press.
  Zentralblatt MATH: 0992.91036
  
• Smoller, J. (1994). Shock Waves and Reaction-Diffusion Equations. Springer, Berlin.
  Mathematical Reviews (MathSciNet): MR1301779
  Zentralblatt MATH: 0807.35002
  
• Steffensen, M. (2000). A no arbitrage approach to Thiele's differential equation. Insurance Math. Econom. 27 201–214.
  Zentralblatt MATH: 0994.91032
  Digital Object Identifier: doi:10.1016/S0167-6687(00)00048-2