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.
Referenze Bibliografiche
[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 329726 |
Zbl 0276.93060[3]
T. BJÖRK,
Arbitrage Theory in Continuous Time,
Oxford University Press (
1998). |
Zbl 1140.91038[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 1841719 |
Zbl 0993.91018[6]
F. DELBAEN-
W. SCHACHERMAYER,
A General Version of the Fundamental Theorem of Asset Pricing,
Math. Annalen,
300 (
1994), 463-520. |
MR 1304434 |
Zbl 0865.90014[7]
F. DELBAEN-
W. SCHACHERMAYER,
The Fundamental Theorem of Asset Pricing for Unbounded Stochastic Processes,
Mathematische Annalen,
312 (
1998), 215-250. |
MR 1671792 |
Zbl 0917.60048[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 1311659 |
Zbl 0831.90010[9]
P. GUASONI-
W. SCHACHERMAYER,
Necessary Conditions for the Existence of Utility Maximizing Strategies under Transaction Costs, Preprint (
2003). |
MR 2108327 |
Zbl 1124.91336[10]
P. GUASONI-
M. DE DONNO-
M. PRATELLI,
Super-replication and Utility Maximization in Large Financial Markets, Preprint (
2003). |
Zbl 1081.60051[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 1089152 |
Zbl 0733.93085[12]
J. KOMLOS,
A generalization of a problem of Steinhaus,
Acta Math. Sci. Hung.,
18 (
1967), 217-229. |
MR 210177 |
Zbl 0228.60012[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 1722287 |
Zbl 0967.91017[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 456373 |
Zbl 1011.91502[16]
R. C. MERTON,
Continuous-Time Finance,
Basil Blackwell, Oxford (
1990). |
Zbl 1019.91502[18]
P. PROTTER,
Stochastic Integration and differential equations,
Springer, Berlin, Heidelberg, New York (
1990). |
MR 1037262 |
Zbl 0694.60047[19]
R. T. ROCKAFELLAR,
Convex Analysis,
Princeton University Press, Princeton, New Jersey (
1970). |
MR 274683 |
Zbl 0193.18401[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 1960575 |
Zbl 1002.91033[22]
W. SCHACHERMAYER,
Portfolio Optimization in Incomplete Financial Markets, apparirà nella collana «
Pubblicazioni della Scuola Normale Superiore» (
2003). |
MR 2144570 |
Zbl 1104.91042[23]
H. STRASSER,
Mathematical theory of statistics: statistical experiments and asymptotic decision theory,
De Gruyter studies in mathematics, Vol.
7 (
1985). |
MR 812467 |
Zbl 0594.62017[24]
N. TOUZI,
Stochastic control problems, viscosity solutions, and application to Finance, apparirà nella collana «
Pubblicazioni della Scuola Normale Superiore» (
2003). |
MR 2100161 |
Zbl 1076.93001