Geodesic
Alcuni problemi matematici legati alla gestione ottima di un portafoglio
Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 3, pp. 593-607.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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.
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. 
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Pratelli, Maurizio. Alcuni problemi matematici legati alla gestione ottima di un portafoglio. Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 3, pp. 593-607. http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_3_a3/

[1] A. Andreotti-G. Tomassini, Spazi vettoriali topologici, Quaderni dell'Unione Matematica Italiana, Pitagora Editrice, Bologna (1978).

[2] J. M. Bismut, Conjugate convex functions in optimal stochastic control, J. Math. Anal. Appl., 44 (1973), 384-404. | MR | Zbl

[3] T. Björk, Arbitrage Theory in Continuous Time, Oxford University Press (1998). | Zbl

[4] W. Brannath-W. Schachermayer, A Bipolar Theorem for Subsets of $L^0$, Séminaire de Probabilités, XXXIII (1999), 349-354. | fulltext mini-dml | MR | Zbl

[5] J. Cvitanic-W. Schachermayer-H. Wang, Utility Maximization in Incomplete Markets with Random Endowment, Finance and Stochastics, 5, No. 2 (2001), 259-272. | MR | Zbl

[6] F. Delbaen-W. Schachermayer, A General Version of the Fundamental Theorem of Asset Pricing, Math. Annalen, 300 (1994), 463-520. | MR | Zbl

[7] F. Delbaen-W. Schachermayer, The Fundamental Theorem of Asset Pricing for Unbounded Stochastic Processes, Mathematische Annalen, 312 (1998), 215-250. | MR | Zbl

[8] N. El Karoui-M. C. Quenez, Dynamic programming and pricing of contingent claims in an incomplete market, SIAM Journal on Control and Optimization, 33 (1995), 29-66. | MR | Zbl

[9] P. Guasoni-W. Schachermayer, Necessary Conditions for the Existence of Utility Maximizing Strategies under Transaction Costs, Preprint (2003). | MR | Zbl

[10] P. Guasoni-M. De Donno-M. Pratelli, Super-replication and Utility Maximization in Large Financial Markets, Preprint (2003). | Zbl

[11] I. Karatzas-J. P. Lehoczky-S. E. Shreve-G. L. Xu, Martingale and duality methods for utility maximization in an incomplete market, SIAM Journal of Control and Optimization, 29 (1991), 702-730. | MR | Zbl

[12] J. Komlos, A generalization of a problem of Steinhaus, Acta Math. Sci. Hung., 18 (1967), 217-229. | MR | Zbl

[13] D. Kramkov-W. Schachermayer, The Asymptotic Elasticity of Utility Functions and Optimal Investment in Incomplete Markets, Annals of Applied Probability, 9, No. 3 (1999), 904-950. | fulltext mini-dml | MR | Zbl

[14] R. C. Merton, Lifetime portfolio selection under uncertainty: the continuous-time model, Rev. Econom. Statist., 51 (1969), 247-257.

[15] R. C. Merton, Optimum consumption and portfolio rules in a continuous-time model, Journal of Economic Theory, 3 (1971), 373-413. | MR | Zbl

[16] R. C. Merton, Continuous-Time Finance, Basil Blackwell, Oxford (1990). | Zbl

[17] M. Pratelli, A minimax theorem without compactness hypothesis, Preprint (2004). | MR | Zbl

[18] P. Protter, Stochastic Integration and differential equations, Springer, Berlin, Heidelberg, New York (1990). | MR | Zbl

[19] R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, New Jersey (1970). | MR | Zbl

[20] P. A. Samuelson, Lifetime portfolio selection by dynamic stochastic programming, Rev. Econom. Statist., 51 (1969), 239-246.

[21] W. Schachermayer, 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. | MR | Zbl

[22] W. Schachermayer, Portfolio Optimization in Incomplete Financial Markets, apparirà nella collana «Pubblicazioni della Scuola Normale Superiore» (2003). | MR | Zbl

[23] H. Strasser, Mathematical theory of statistics: statistical experiments and asymptotic decision theory, De Gruyter studies in mathematics, Vol. 7 (1985). | MR | Zbl

[24] N. Touzi, Stochastic control problems, viscosity solutions, and application to Finance, apparirà nella collana «Pubblicazioni della Scuola Normale Superiore» (2003). | MR | Zbl