Multivariate utility maximization with proportional transaction costs

Finance and Stochastics

Volumn 15, Issue 3, 2011, Pages 461-499

  Campi, Luciano ^a   Owen, Mark P ^b  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

^b HERIOT WATT UNIVERSITY   (United Kingdom)

Author keywords

Asymptotic satiability; Duality theory; Foreign exchange market; Lagrange duality; Multivariate utility function; Optimal portfolio; Transaction costs

Indexed keywords

EID: 80051996198     PISSN: 09492984     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00780-010-0125-9     Document Type: Article

References (34)

1. Aliprantis, C. D., Border, K. C.: Infinite Dimensional Analysis: A Hitchhiker's Guide, 3rd edn. Springer, Berlin (2006).
2. Bouchard, B.: Utility maximization on the real line under proportional transaction costs. Finance Stoch. 6, 495-516 (2002).
3. Bouchard, B., Pham, H.: Optimal consumption in discrete time financial models with industrial investment opportunities and non-linear returns. Ann. Appl. Probab. 15, 2393-2421 (2005).
4. Campi, L., Schachermayer, W.: A super-replication theorem in Kabanov's model of transaction costs. Finance Stoch. 10, 579-596 (2006).
5. Cvitanić, J., Karatzas, I.: Hedging and portfolio optimization under transaction costs: a martingale approach. Math. Finance 6, 133-165 (1996).
6. Cvitanić, J., Wang, H.: On optimal wealth under transaction costs. J. Math. Econ. 35, 223-231 (2001).
7. Cvitanić, J., Schachermayer, W., Wang, H.: Utility maximization in incomplete markets with random endowment. Finance Stoch. 5, 259-272 (2001).
8. Davis, M. H. A., Norman, A. R.: Portfolio selection with transaction costs. Math. Oper. Res. 15, 676-713 (1990).
9. Deelstra, G., Pham, H., Touzi, N.: Dual formulation of the utility maximization problem under transaction costs. Ann. Appl. Probab. 11, 1353-1383 (2001).
10. Diestel, J., Uhl, J. J.: Vector Measures. Mathematical Surveys, vol. 15. American Mathematical Society, Providence (1977).
11. Dunford, N., Schwartz, J. T.: Linear Operators. Part I: General Theory. Interscience, New York (1964).
12. Guasoni, P., Rásonyi, M.: The fundamental theorem of asset pricing under transaction costs. Finance Stoch. (forthcoming).
13. Guasoni, P., Rásonyi, M., Schachermayer, W.: The fundamental theorem of asset pricing for continuous processes under small transaction costs. Ann. Finance (forthcoming). Available at http://www. springerlink. com/content/336w847222440318/?p=a89f53ac22794f3d9d24bc2df8cb320c&pi=13.
14. Jouini, E., Kallal, H.: Martingales and arbitrage in securities markets with transaction costs. J. Econ. Theory 66, 178-197 (1995).
15. Kabanov, Yu. M.: Hedging and liquidation under transaction costs in currency markets. Finance Stoch. 3, 237-248 (1999).
16. Kabanov, Yu. M., Last, G.: Hedging under transaction costs in currency markets: a continuous time model. Math. Finance 12, 63-70 (2002).
17. 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, pp. 125-136. Springer, Berlin (2002).
18. 0 and the robust no-arbitrage property. Finance Stoch. 7, 403-411 (2003).
19. Kamizono, K.: Hedging and optimization under transaction costs. Ph. D. Thesis, Columbia University (2001). Available at http://app. cul. columbia. edu: 8080/ac/handle/10022/AC: P: 4525.
20. Kamizono, K.: Multivariate utility maximization under transaction costs. In: Akahori, J., Ogawa, S., Watanabe, S. (eds.) Stochastic Processes and Applications to Mathematical Finance: Proceedings of the Ritsumeikan International Symposium, pp. 133-149. World Scientific, Singapore (2004).
21. Karatzas, I., Žitković, G.: Optimal consumption from investment and random endowment in incomplete semimartingale markets. Ann. Probab. 31, 1821-1858 (2003).
22. Klein, I., Rogers, L. C. G.: Duality in optimal investment and consumption problems with market frictions. Math. Finance 17, 225-247 (2007).
23. Kramkov, D., Schachermayer, W.: The asymptotic elasticity of utility functions and optimal investment in incomplete markets. Ann. Appl. Probab. 9, 904-950 (1999).
24. Kramkov, D., Schachermayer, W.: Necessary and sufficient conditions in the problem of optimal investment in incomplete markets. Ann. Appl. Probab. 13, 1504-1516 (2003).
25. Lakner, P.: Consumption/investment and equilibrium in the presence of several commodities. Ph. D. Thesis, Columbia University (1989).
26. Luenberger, D. G.: Optimization by Vector Space Methods. Wiley, New York (1969).
27. Müller, A., Stoyan, D.: Comparison Methods for Stochastic Models and Risks. Wiley, New York (2002).
28. Owen, M. P., Žitković, G.: Optimal investment with an unbounded random endowment and utility-based pricing. Math. Finance 19, 129-159 (2009).
29. Rao, K. P. S. B., Rao, M. B.: Theory of Charges: A Study of Finitely Additive Measures. Academic Press, London (1983).
30. Richard, S. F.: Multivariate risk aversion, utility independence and separable utility functions. Manag. Sci. 22, 12-21 (1975).
31. Rockafellar, R. T.: Convex Analysis. Princeton University Press, Princeton (1972).
32. Schachermayer, W.: The fundamental theorem of asset pricing under proportional transaction costs in finite discrete time. Math. Finance 14, 19-48 (2004).
33. Shreve, S. E., Soner, H. M.: Optimal investment and consumption with transaction costs. Ann. Appl. Probab. 4, 609-692 (1994).
34. Zǎlinescu, C.: Convex Analysis in General Vector Spaces. World Scientific, New Jersey (2002).