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.
@article{BUMI_2004_8_7B_3_593_0, author = {Maurizio Pratelli}, title = {Alcuni problemi matematici legati alla gestione ottima di un portafoglio}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {7-A}, year = {2004}, pages = {593-607}, zbl = {1182.91075}, mrnumber = {2101653}, language = {it}, url = {http://dml.mathdoc.fr/item/BUMI_2004_8_7B_3_593_0} }
Pratelli, Maurizio. Alcuni problemi matematici legati alla gestione ottima di un portafoglio. Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004) pp. 593-607. http://gdmltest.u-ga.fr/item/BUMI_2004_8_7B_3_593_0/
[1]
- , Spazi vettoriali topologici, Quaderni dell'Unione Matematica Italiana, Pitagora Editrice, Bologna (1978).[2] Conjugate convex functions in optimal stochastic control, J. Math. Anal. Appl., 44 (1973), 384-404. | MR 329726 | Zbl 0276.93060
,[3] | Zbl 1140.91038
, Arbitrage Theory in Continuous Time, Oxford University Press (1998).[4] A Bipolar Theorem for Subsets of , Séminaire de Probabilités, XXXIII (1999), 349-354. | MR 1768009 | Zbl 0957.46020
- ,[5] Utility Maximization in Incomplete Markets with Random Endowment, Finance and Stochastics, 5, No. 2 (2001), 259-272. | MR 1841719 | Zbl 0993.91018
- - ,[6] A General Version of the Fundamental Theorem of Asset Pricing, Math. Annalen, 300 (1994), 463-520. | MR 1304434 | Zbl 0865.90014
- ,[7] The Fundamental Theorem of Asset Pricing for Unbounded Stochastic Processes, Mathematische Annalen, 312 (1998), 215-250. | MR 1671792 | Zbl 0917.60048
- ,[8] Dynamic programming and pricing of contingent claims in an incomplete market, SIAM Journal on Control and Optimization, 33 (1995), 29-66. | MR 1311659 | Zbl 0831.90010
- ,[9] Necessary Conditions for the Existence of Utility Maximizing Strategies under Transaction Costs, Preprint (2003). | MR 2108327 | Zbl 1124.91336
- ,[10] Super-replication and Utility Maximization in Large Financial Markets, Preprint (2003). | Zbl 1081.60051
- - ,[11] Martingale and duality methods for utility maximization in an incomplete market, SIAM Journal of Control and Optimization, 29 (1991), 702-730. | MR 1089152 | Zbl 0733.93085
- - - ,[12] A generalization of a problem of Steinhaus, Acta Math. Sci. Hung., 18 (1967), 217-229. | MR 210177 | Zbl 0228.60012
,[13] The Asymptotic Elasticity of Utility Functions and Optimal Investment in Incomplete Markets, Annals of Applied Probability, 9, No. 3 (1999), 904-950. | MR 1722287 | Zbl 0967.91017
- ,[14] Lifetime portfolio selection under uncertainty: the continuous-time model, Rev. Econom. Statist., 51 (1969), 247-257.
,[15] Optimum consumption and portfolio rules in a continuous-time model, Journal of Economic Theory, 3 (1971), 373-413. | MR 456373 | Zbl 1011.91502
,[16] | Zbl 1019.91502
, Continuous-Time Finance, Basil Blackwell, Oxford (1990).[17] A minimax theorem without compactness hypothesis, Preprint (2004). | MR 2135081 | Zbl 1150.49009
,[18] | MR 1037262 | Zbl 0694.60047
, Stochastic Integration and differential equations, Springer, Berlin, Heidelberg, New York (1990).[19] | MR 274683 | Zbl 0193.18401
, Convex Analysis, Princeton University Press, Princeton, New Jersey (1970).[20] Lifetime portfolio selection by dynamic stochastic programming, Rev. Econom. Statist., 51 (1969), 239-246.
,[21] Optimal Investment in Incomplete Financial Markets, Mathematical Finance: Bachelier Congress 2000 ( , , , , editors), Springer (2001), 427-462. | MR 1960575 | Zbl 1002.91033
,[22] Portfolio Optimization in Incomplete Financial Markets, apparirà nella collana «Pubblicazioni della Scuola Normale Superiore» (2003). | MR 2144570 | Zbl 1104.91042
,[23] Mathematical theory of statistics: statistical experiments and asymptotic decision theory, De Gruyter studies in mathematics, Vol. 7 (1985). | MR 812467 | Zbl 0594.62017
,[24] Stochastic control problems, viscosity solutions, and application to Finance, apparirà nella collana «Pubblicazioni della Scuola Normale Superiore» (2003). | MR 2100161 | Zbl 1076.93001
,