A geometric approach to portfolio optimization in models with transaction costs

Finance and Stochastics

Volumn 8, Issue 2, 2004, Pages 207-227

  Kabanov, Yuri ^a,b   Klüppelberg, Claudia ^c  

^a UNIVERSITÉ DE FRANCHE COMTÉ   (France)

^b CENTRAL ECONOMICS AND MATHEMATICS INSTITUTE   (Russian Federation)

^c TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Consumption investment problem; Currency market; HJB equation; Transaction costs; Utility function; Viscosity solution

Indexed keywords

EID: 24144452773     PISSN: 09492984     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00780-003-0114-3     Document Type: Article

References (26)

1. Akian, M., Menaldi, J.L., Sulem, A.: On an investment-consumption model with transaction costs. SIAM J. Control Opt. 34(1), 329-364 (1996)
2. Akian, M., Sulem, A., Taksar, M.I.: Dynamic optimization of long-term growth rate for a portfolio with transaction costs and logarithmic utility. Math. Finance 11(2), 153-188 (2001)
3. Aubin, J.-B.: Optima and equilibria. An Introduction to Nonlinear Analysis. Berlin Heidelberg New York: Springer 1993
4. Bank, P., Riedel, F.: Optimal consumption choice under uncertainty with intertemporal substitution. Ann. Appl. Probab. 11(3), 750-788 (2001)
5. Bardi, M., Capuzzo-Dolcetta, I.: Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Boston: Birkhäuser 1997
6. Benth, F.E., Karlsen K.H., Reikvam K.: Optimal portfolio selection with consumption and nonlinear integro-differential equations with gradient constraint: A viscosity solution approach. Finance Stochast. 5(3), 275-303 (2001)
7. Benth F.E., Karlsen, K.H., Reikvam, K.: Portfolio optimization in a Lévy market with intertemporal substitution and transaction costs. Stochast. Stochast. Reports 74(3-4), 517-569 (2002)
8. Cadenillas, A.: Consumption-investment problems with transaction costs: survey and open problems. Math. Meth. Oper. Res. 51(1), 43-68 (2000)
9. Crandall, M.G., Ishii, H., Lions, P.-L.: User's guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. 27(1), 1-67 (1992)
10. Davis, M., Norman, A.: Portfolio selection with transaction costs. Math. Oper. Res. 15, 676-713 (1990)
11. Davis, M., Panas, Zariphopoulou, T.: European option pricing with transaction costs. SIAM J. Control Opt. 31, 470-493 (1993)
12. Deelstra, G., Pham, H., Touzi, N.: Dual formulation of the utility maximazition problem under transaction costs. Ann. Appl. Probab. 11 (4), 1353-1383 (2001)
13. Delbaen, F., Kabanov, Yu.M, Valkeila, S.: Hedging under transaction costs in currency markets: a discrete-time model. Math. Finance 12(1), 45-61 (2002)
14. Emmer, S., Klüppelberg, C.: Optimal portfolios when stock prices follow an exponential Lévy process. Finance Stochast. 8, 17-44 (2004)
15. Framstadt, N.Chr., Øksendal, B., Sulem, A.: Optimal consumption and portfolio in a jump-diffusion market with proportional transaction costs. J. Math. Econ. 35(2), 233-257 (2001)
16. Fleming, W.H., Soner, M.: Controlled Markov processes and viscosity solutions. Berlin Heidelberg New York: Springer 1993
17. Kabanov, Yu.M.: Hedging and liquidation under transaction costs in currency markets. Finance Stochast. 3(2), 237-248 (1999)
18. Kabanov Yu.M.: The arbitrage theory. In: Jouini, E., Cvitanić, J., Musiela, M. (eds.) Handbooks in mathematical finance: Topics in option pricing, interest rates and risk management. Cambridge: Cambridge University Press 2001
19. Kabanov, Yu.M., Last, G.: Hedging under transaction costs in currency markets: a continuous-time model. Math. Finance 12(1), 73-70 (2002)
20. Kabanov, Yu.M., Stricker, Ch.: Hedging of contingent claims under transaction costs. In: Sandmann, K., Schönbucher, Ph. (eds.) Advances in finance and stochastics. Essays in honour of Dieter Sondermann. Berlin Heidelberg New York: Springer 2002
21. Magill, M.J.P., Constantinides, G.M.: Portfolio selection with transaction costs. J. Econ. Theory 13, 245-263 (1976)
22. Shreve, S., Soner, M.: Optimal investment and consumption with transaction costs. Ann. Appl. Probab. 4(3), 609-692 (1994)
23. Tourin A., Zariphopoulou, T.: Portfolio selections with transaction costs. Progress Probab. 36, 287-307 (1995)
24. Yong, J., Zhou, X.Y.: Stochastic controls. Hamiltonian systems and HJB equations. Berlin Heidelberg New York: Springer 1999
25. Zariphopoulou, T.: Investment-consumption models with transaction fees and Markov-chain parameters. SIAM J. Control Opt. 30(3), 613-636 (1992)
26. Zariphopoulou, T.: Transaction cost in portfolio menagement and derivative pricing. In: Introduction to Mathematical Finance, 101-163. Proc. Sympos. Appl. Math. 57, Providence, RI: AMS 1999