I. Introduzione. II. Un rapido esame di modelli e strumenti. III. Simulazioni Monte-Carlo efficienti e calcolo di Malliavin. IV. Osservazioni parziali e «option pricing».
@article{BUMI_2000_8_3B_3_553_0, author = {P. L. Lions}, title = {On mathematical finance}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {3-A}, year = {2000}, pages = {553-572}, zbl = {0960.91040}, mrnumber = {1801617}, language = {en}, url = {http://dml.mathdoc.fr/item/BUMI_2000_8_3B_3_553_0} }
Lions, P. L. On mathematical finance. Bollettino dell'Unione Matematica Italiana, Tome 3-A (2000) pp. 553-572. http://gdmltest.u-ga.fr/item/BUMI_2000_8_3B_3_553_0/
[1] Pricing and hedging derivative securities inmarckets with uncertain volatilities, Appl. Math. Finance, 2 (1995), 73-88.
- - ,[2]
- - , preprint.[3] Option pricing with transaction costs and a nonlinearBlack-Scholes equation, Finance and Stochastics, to appear. | Zbl 0915.35051
- ,[4] The pricing of options and corporate liabilities, J. Political Economy, 81 (1973), 637-659. | Zbl 1092.91524
- ,[5] Valuation of mortgage-backed securitiesusing Brownian bridges to reduce effective dimension, J. Comp. Finance, 1 (1997),27-46.
- - ,[6] | MR 955269 | Zbl 0661.90001
, Security Markets: Stochastics Models, Academic Press, Boston, 1988.[7] | Zbl 1140.91041
, Dynamic Asset Pricing Theory, 2nd edit., Princeton Univ. Press, Princeton, 1996.[8] Applications of Malliavin calculus to Monte-Carlo methods in Finance, Finance and Stochastics, 3 (1999). | MR 1842285 | Zbl 0947.60066
- - - - ,[9] Applications of Malliavincalculus to Monte-Carlo methods in Finance, II, Finance and Stochastics, toappear. | Zbl 0973.60061
- - - ,[10] Introduction au calcul stochastique appliquè a la Finance, 1991. | Zbl 0497.60055
- ,[11]
- , work in preparation.[12] Control stochastique avec informations partielles et applicationsa la Finance, C.R. Acad. Sci. Paris, 328 (1999), 1003-1010. | MR 1696196 | Zbl 0937.93058
- ,[13] Viscosity solutions of fully nonlinear second order equations and optimalstochastic control in infinite dimension, Part II: Optimal control of Zakai'sequation. In Stochastic Partial Differential Equations and Applications, II. SpringerL.N. Maths, 1340, Berlin, 1989. | MR 1019600 | Zbl 0757.93083
,[14]
- , work in preparation.[15] | MR 1450093 | Zbl 0878.60001
, Stochastic Analysis, Springer, Berlin, 1997.[16] Theory of rational option pricing, Bell J. Econom. Manag. Sci, 4 (1973), 141-183. | MR 496534
,[17] | MR 1474500 | Zbl 0906.60001
- , Mastingale methods in Financial Modelling, Springer, Berlin, 1997.[18] | MR 1344217 | Zbl 0837.60050
, The Malliavin calculus and related topics, Springer, Berlin, 1995.[19] | Zbl 0992.91500
, Interest rate option models, Wiley, New-York, 1997.