Abstract
We discuss existing and new results for mathematical finance models with transaction costs, namely models of portfolio management and international asset pricing in the presence of political risk. The main analysis comes from the theories of singular stochastic control and viscosity solutions for first and second order nonlinear partial differential equations.
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References
Capuzzo-Dolcetta, I., P.-L. Lions, P.-L. (1990). Viscosity solutions of Ham-Uton-Jacobi equations. Trans. Amer. Math. Soc, 318, pp 643–683.
Constantinides, G. M., Zariphopoulou, T. (1998). Bounds on prices of derivative securities in an intertemporal setting with proportional transaction costs and multiple securities, working paper.
Constantinides, G. M., Zariphopoulou, T. (1997). Bounds on prices of contingent claims in an intertemporal economy with proportional transaction costs and general preferences, submitted for publication.
Crandall, M., Ishii, H., Lions, P.-L. (1992). User’s guide to viscosity solutions of second order partial differential equations. Bulletin of the American Mathematical Society, 27, pp 1–67.
Crandall, M., Lions, P.-L. (1983). Viscosity solutions of Hamilton-Jacobi equations. Transactions of the American Mathematical Society, 277, pp 1–42.
Davis, M. H. A., Norman, A. R. (1990). Portfolio selection with transaction costs. Mathematics of Operations Research, 15, pp 676–713.
Davis, M. H. A., Panas, V. G., Zariphopoulou, T. (1993). European option pricing with transaction costs. SIAM J. of Control and Optimization, 31, pp 470–493.
Davis, M. H. A., Zariphopoulou, T. (1995). American Options and Transaction Fees. Mathematical Finance, Springer-Verlag.
Dumas, B. (1992). Dynamic Equilibrium and the Real Exchange Rate in a Spatially Separated World, Review of Financial Studies, 5, pp 153–180.
Fleming, W., Soner, H. M. (1993). Controlled Markov Processes and Viscosity Solutions. Springer-Verlag, New York.
Hodder, J. E., Tourin, A., Zariphopoulou, T. (1998). Numerical schemes for variational inequalities arising in international price models, in preparation.
Hodges, S. D., Neuberger, A. (1989). Optimal replication of contingent claims under transaction costs. Review of Futures Markets, 8, pp 222–239.
Ishii, H., Lions, P.-L. (1990). Viscosity solutions of fully nonlinear second-order elliptic partial differential equations. Journal of Differential Equations, 83, pp 26–78.
Lions, P.-L. (1983). Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations. Part 1: The dynamic programming principle and applications. Part 2: Viscosity solutions and uniqueness.Communications in PDE, 8, pp 1101–1174 and pp 1229-12
Pichler, A. (1996). On transaction costs and HJB equations. Preprint.
Shreve, S. E., Soner, H. M. (1994). Optimal investment and consumption with transaction costs. The Annals of Applied Probability, 4, pp 609–692.
Soner, H. M. (1986). Optimal control with state space constraints. SIAM Journal of Control and Optimization, 24, pp 552–562, pp 1110-1122.
Tourin, A., Zariphopoulou, T. (1994). Numerical schemes for investment models with singular transactions. Computational Economics, 7, pp 287–307.
Tourin, A., Zariphopoulou, T. (1995). Portfolio Selection with Transaction Costs, Progress in Probability, 4.
Zariphopoulou, T. (1992). Investment-consumption models with transaction fees and Markov-chain parameters. SIAM Journal of Control and Optimization, 30, pp 613–636.
Zariphopoulou, T. (1994). Investment consumption models with constraints, SIAM Journal of Control and Optimization, 32, pp 59–84.
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Hodder, J.E., Zariphopoulou, T. (1999). Pricing Models with Transaction Fees. In: McEneaney, W.M., Yin, G.G., Zhang, Q. (eds) Stochastic Analysis, Control, Optimization and Applications. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1784-8_34
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DOI: https://doi.org/10.1007/978-1-4612-1784-8_34
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7281-6
Online ISBN: 978-1-4612-1784-8
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