Obstacle problem for nonlinear integro-differential equations arising in option pricing

Ricerche di Matematica

Volumn 56, Issue 1, 2007, Pages 1-17

  Amadori, Anna Lisa ^a  

^a UNIVERSITY OF NAPLES PARTHENOPE   (Italy)

Author keywords

American options; Integro differential equations; Obstacle problem; Viscosity solutions

Indexed keywords

EID: 34848819098     PISSN: 00355038     EISSN: 18273491     Source Type: Journal    
DOI: 10.1007/s11587-007-0001-x     Document Type: Article

References (17)

1. Alvarez, O., Tourin, A.: Viscosity solutions of nonlinear integro-differential equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 13, 293-317 (1996)
2. Amadori, A.L., Karlsen, K.H., La Chioma, C.: Non-linear degenerate integro-partial differential evolution equations related to geometric Lévy processes and applications to backward stochastic differential equations. Stoch. Stoch. Rep. 76, 147-177 (2004)
3. Amadori, A.L.: Nonlinear integro-differential evolution problems arising in option pricing: a viscosity solutions approach. Differ. Integral Eq. 7, 787-811 (2003)
4. Barles, G., Buckdahn, R., Pardoux, E.: Backward stochastic differential equations and integral-partial differential equations. Stoch. Stoch. Rep. 60, 57-83 (1997)
5. Barles, G., Perthame, B.: Exit time problems in optimal control and vanishing viscosity method. SIAM J. Control Optim. 26, 1133-1148 (1988)
6. Barles, G., Perthame, B.: Comparison principle for Dirichlet-type Hamilton-Jacobi equations and singular perturbation of degenerated elliptic equations. Appl. Math. Optim. 21, 21-44 (1990)
7. Bardi, M., Capuzzo Dolcetta, I.: Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Birkhäuser, Boston (1997)
8. Crandall, M.G., Ishii, H., Lions, P.-L.: Users' guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. 27, 1-67 (1992)
9. Cvitanic, J., Ma J.: Hedging options for a large investor and forward-backward SDE's. Ann. Appl. Probab. 6(2), 370-398 (1996)
10. Garroni, M.G., Menaldi J.L.: Green functions for second order parabolic integrodifferential problems. Pitman Research Notes in Mathematics Series 275, Longman Scientific & Technical, Harlow (1992)
11. Ishii, H., Kobayasi, K.: On the uniqueness and existence of solutions of fully nonlinear parabolic PDEs under the Osgood type condition. Differ. Integral Eq. 7, 909-920 (1994)
12. Jeanblanc-Piquè, M., Pointier, M.: Optimal portfolio for a small investor in a market model with discontinuous prices. Appl. Math. Opt. 22, 287-310 (1990)
13. Kampen, J.: On American derivatives and related obstacle problems. Int. J. Theor. Appl. Finance 6(6), 565-591 (2003)
14. Mastroeni, L., Matzeu, M.: Nonlinear variational inequalities for jump-diffusion process and irregular obstacles with a financial application. Nonlin. Anal. 34, 889-905 (1998)
15. Pham, H.: Optimal stopping, free boundary, and American option in a jump-diffusion model. Appl. Math. Optim. 35(2), 145-164 (1997)
16. Pham. H.: Optimal stopping of controlled jump diffusion processes: a viscosity solution approach. J. Math. Systems Estim. Control 8(1) 27 pp. (electronic), (1998)
17. Runggaldier, W.J.: Jump Diffusion Models. In: Handbook of Heavy Tailed Distributions in Finance (S.T. Rachev, ed.) 169-209, Handbooks in Finance, Book 1 (W.Ziemba Series Ed.), Elesevier/North-Holland (2003)