Alcuni problemi matematici legati alla gestione ottima di un portafoglio

Maurizio Pratelli

Bollettino dell'Unione Matematica Italiana (2004)

  • Volume: 7-B, Issue: 3, page 593-607
  • ISSN: 0392-4041

Abstract

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In this talk, main ideas concerning the classic problem of portfolio optimization (also known as Merton's problem) are illustrated. Methods of stochastic control are compared to those of infinite-dimensional convex duality.

How to cite

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Pratelli, Maurizio. "Alcuni problemi matematici legati alla gestione ottima di un portafoglio." Bollettino dell'Unione Matematica Italiana 7-B.3 (2004): 593-607. <http://eudml.org/doc/195232>.

@article{Pratelli2004,
abstract = {In questa conferenza, vengono esposte le idee essenziali che stanno alla base del classico problema di gestire un portafoglio in modo da rendere massima l'utilità media. I metodi tipici del controllo stocastico sono confrontati con le idee della dualità convessa infinito-dimensionale.},
author = {Pratelli, Maurizio},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {ita},
month = {10},
number = {3},
pages = {593-607},
publisher = {Unione Matematica Italiana},
title = {Alcuni problemi matematici legati alla gestione ottima di un portafoglio},
url = {http://eudml.org/doc/195232},
volume = {7-B},
year = {2004},
}

TY - JOUR
AU - Pratelli, Maurizio
TI - Alcuni problemi matematici legati alla gestione ottima di un portafoglio
JO - Bollettino dell'Unione Matematica Italiana
DA - 2004/10//
PB - Unione Matematica Italiana
VL - 7-B
IS - 3
SP - 593
EP - 607
AB - In questa conferenza, vengono esposte le idee essenziali che stanno alla base del classico problema di gestire un portafoglio in modo da rendere massima l'utilità media. I metodi tipici del controllo stocastico sono confrontati con le idee della dualità convessa infinito-dimensionale.
LA - ita
UR - http://eudml.org/doc/195232
ER -

References

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  1. ANDREOTTI, A.- TOMASSINI, G., Spazi vettoriali topologici, Quaderni dell'Unione Matematica Italiana, Pitagora Editrice, Bologna (1978). 
  2. BISMUT, J. M., Conjugate convex functions in optimal stochastic control, J. Math. Anal. Appl., 44 (1973), 384-404. Zbl0276.93060MR329726
  3. BJÖRK, T., Arbitrage Theory in Continuous Time, Oxford University Press (1998). Zbl1140.91038
  4. BRANNATH, W.- SCHACHERMAYER, W., A Bipolar Theorem for Subsets of L 0 , Séminaire de Probabilités, XXXIII (1999), 349-354. Zbl0957.46020MR1768009
  5. CVITANIC, J.- SCHACHERMAYER, W.- WANG, H., Utility Maximization in Incomplete Markets with Random Endowment, Finance and Stochastics, 5, No. 2 (2001), 259-272. Zbl0993.91018MR1841719
  6. DELBAEN, F.- SCHACHERMAYER, W., A General Version of the Fundamental Theorem of Asset Pricing, Math. Annalen, 300 (1994), 463-520. Zbl0865.90014MR1304434
  7. DELBAEN, F.- SCHACHERMAYER, W., The Fundamental Theorem of Asset Pricing for Unbounded Stochastic Processes, Mathematische Annalen, 312 (1998), 215-250. Zbl0917.60048MR1671792
  8. EL KAROUI, N.- QUENEZ, M. C., Dynamic programming and pricing of contingent claims in an incomplete market, SIAM Journal on Control and Optimization, 33 (1995), 29-66. Zbl0831.90010MR1311659
  9. GUASONI, P.- SCHACHERMAYER, W., Necessary Conditions for the Existence of Utility Maximizing Strategies under Transaction Costs, Preprint (2003). Zbl1124.91336MR2108327
  10. GUASONI, P.- DE DONNO, M.- PRATELLI, M., Super-replication and Utility Maximization in Large Financial Markets, Preprint (2003). Zbl1081.60051
  11. KARATZAS, I.- LEHOCZKY, J. P.- SHREVE, S. E.- XU, G. L., Martingale and duality methods for utility maximization in an incomplete market, SIAM Journal of Control and Optimization, 29 (1991), 702-730. Zbl0733.93085MR1089152
  12. KOMLOS, J., A generalization of a problem of Steinhaus, Acta Math. Sci. Hung., 18 (1967), 217-229. Zbl0228.60012MR210177
  13. KRAMKOV, D.- SCHACHERMAYER, W., The Asymptotic Elasticity of Utility Functions and Optimal Investment in Incomplete Markets, Annals of Applied Probability, 9, No. 3 (1999), 904-950. Zbl0967.91017MR1722287
  14. MERTON, R. C., Lifetime portfolio selection under uncertainty: the continuous-time model, Rev. Econom. Statist., 51 (1969), 247-257. 
  15. MERTON, R. C., Optimum consumption and portfolio rules in a continuous-time model, Journal of Economic Theory, 3 (1971), 373-413. Zbl1011.91502MR456373
  16. MERTON, R. C., Continuous-Time Finance, Basil Blackwell, Oxford (1990). Zbl1019.91502
  17. PRATELLI, M., A minimax theorem without compactness hypothesis, Preprint (2004). Zbl1150.49009MR2135081
  18. PROTTER, P., Stochastic Integration and differential equations, Springer, Berlin, Heidelberg, New York (1990). Zbl0694.60047MR1037262
  19. ROCKAFELLAR, R. T., Convex Analysis, Princeton University Press, Princeton, New Jersey (1970). Zbl0193.18401MR274683
  20. SAMUELSON, P. A., Lifetime portfolio selection by dynamic stochastic programming, Rev. Econom. Statist., 51 (1969), 239-246. 
  21. SCHACHERMAYER, W., Optimal Investment in Incomplete Financial Markets, Mathematical Finance: Bachelier Congress 2000 (H. Geman, D. Madan, St.R. Pliska, T. Vorst, editors), Springer (2001), 427-462. Zbl1002.91033MR1960575
  22. SCHACHERMAYER, W., Portfolio Optimization in Incomplete Financial Markets, apparirà nella collana «Pubblicazioni della Scuola Normale Superiore» (2003). Zbl1104.91042MR2144570
  23. STRASSER, H., Mathematical theory of statistics: statistical experiments and asymptotic decision theory, De Gruyter studies in mathematics, Vol. 7 (1985). Zbl0594.62017MR812467
  24. TOUZI, N., Stochastic control problems, viscosity solutions, and application to Finance, apparirà nella collana «Pubblicazioni della Scuola Normale Superiore» (2003). Zbl1076.93001MR2100161

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