In this paper, we relax the assumption of a self-financing strategy in the dynamic investment models. In so doing we provide smooth solutions and constrained viscosity solutions.
References
[1]
M. Alghalith, “A New Stochastic Factor Model: General Ex-plicit Solutions,” Applied Mathematics Letters, Vol. 22, No. 12, 2009, pp. 1852-1854.
doi:10.1016/j.aml.2009.07.011
[2]
N. Castaneda-Leyva and D. Hernandez-Hernandez, “Op- timal Consumption-Investment Problems in Incomplete Markets with Random Coefficients,” Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005, Sevilla, 12-15 December 2005, pp. 6650-6655.
[3]
J. Cvitanic and F. Zapatero, “Introduction to the Economics and Mathematics of Financial Markets,” MIT Press, Cambridge, 2004.
[4]
W. Fleming, “Some Optimal Investment, Production and Con-sumption Models,” Contemporary Mathematics, Vol. 351, 2004, pp. 115-123.
[5]
F. Focardi and F. Fabozzi, “The Mathematics of Financial Modeling and Investment Manage-ment,” Wiley E-Series, 2004.
[6]
F. Minani, “Hausdorff Con-tinuous Viscosity Solutions to Hamilton-Jacobi Equations and their Numerical Analysis,” Unpublished Ph.D. Thesis, Univer-sity of Pretoria, Pretoria, 2007.
