La moderna finanza matematica è un settore interdisciplinare tra economia e matematica che, allo stato attuale, è a forte contenuto matematico, soprattutto probabilistico. Iniziamo questo articolo accennando alle origini di questa disciplina, che non sono molto lontane nel tempo e che erano di natura più economica/econometrica. Successivamente arriveremo a descrivere gli sviluppi più recenti e più tipicamente matematici.
Referenze Bibliografiche
[1] AAVV, Atti del Convegno Ricordo di Bruno de Finetti Professore nell’Ateneo triestino, Dipartimento di Matematica Applicata «Bruno de Finetti», Trieste, 1987.
[3]
K. J. ARROW -
G. DEBREU,
Existence of an equilibrium for a competitive economy,
Econometrica,
22(
1954), 265-290. |
MR 77069 |
Zbl 0055.38007[4]
L. BACHELIER,
Théorie de la spéculation,
Gauthier-Villars 1900. Anche in:
Annales Scientifiques de l’École Normale Supérieure,
1900, 21-86. |
fulltext mini-dml |
Jbk 31.0241.02[5]
P. BALDI,
Equazioni differenziali stocastiche e applicazioni,
Quaderni UMI Vol.
28,
Pitagora, Bologna,
1984. |
Zbl 0606.60051[6]
D.BERNOULLI,
Exposition of a new theory on the measurement of risk, trad. di
E. Sommer in
Econometrica,
22(
1954), 23-36. |
MR 59834 |
Zbl 0055.12004[7]
T. R. BIELECKI -
S. R. PLISKA,
Risk sensitive asset management with transaction costs,
Finance and Stochastics,
4(
2000), 1-33. |
fulltext (doi) |
MR 1790132[8]
T. BJÖRK -
G. DI MASI -
YU. KABANOV -
W. RUNGGALDIER,
Towards a general theory of bond markets,
Finance and Stochastics,
1(
1997), 141-174. |
Zbl 0889.90019[9]
F. BLACK -
M. S. SCHOLES,
The pricing of options and corporate liabilities,
Journal of Political Economy,
81(
1973), 637-654. |
Zbl 1092.91524[11] E. CANESTRELLI - C. NARDELLI, Criteri per la selezione del portafoglio, G. Giappichelli, Torino, 1991.
[12] E. CASTAGNOLI - L. PECCATI, Introduzione alla selezione di portafoglio, Cooperativa di Cultura «Lorenzo Milani», Torino, 1991.
[13]
J.-M. COURTAULT -
YU. KABANOV -
B. BRU -
P. CRÉPEL,
Louis Bachelier on the centenary of Théorie de la Spéculation,
Mathematical Finance,
10 (
2000), 341-353. |
fulltext (doi) |
MR 1800320[14]
J. C. COX -
S. A. ROSS -
M. RUBINSTEIN,
Option pricing: a simplified approach,
Journal of Financial Economics,
7(
1979), 229-263. |
Zbl 1131.91333[16]
J. CVITANIĆ -
H. PHAM -
N. TOUZI,
A closed-form solution to the problem of super-replication under transaction costs,
Finance and Stochastics,
3 (
1999), 35-54. |
Zbl 0924.90010[17]
R. C. DALANG -
A. MORTON -
W. WILLINGER,
Equivalent martingale measures and no-arbitrage in stochastic securities market models,
Stochastics and Stochastic Reports,
29(
1990), 185-201. |
MR 1041035 |
Zbl 0694.90037[20] E. DIMSON - M. MOUSSAVIAN, Three centuries of asset pricing, London Business School, Institute of Finance & Accounting WP-295, Jan 2000.
[21]
D. DUFFIE -
R. KAN,
A yield factor model of interest rates,
Mathematical Finance,
6(
1966), 379-406. |
Zbl 0915.90014[22]
N. ELKAROUI -
M. C. QUENEZ,
Dynamic programming and pricing of contingent claimsin an incomplete market,
SIAM J. on Control and Optimiz.,
33(
1995), 29-66. |
fulltext (doi) |
MR 1311659 |
Zbl 0831.90010[23]
R. E. ENGLE,
Autoregressive conditional heteroskedasticity with estimates of the variance of UK inflation,
Econometrica,
50(
1982), 987-1007. |
fulltext (doi) |
MR 666121 |
Zbl 0491.62099[24] E. F. FAMA, The behaviour of stock market prices, Journal of Business, 38 (1965), 34-105.
[25]
H. FÖLLMER -
P. LEUKERT,
Efficient hedging: cost versus shortfall risk,
Finance and Stochastics,
4(
2000), 117-146. |
fulltext (doi) |
MR 1780323[26]
H. FÖLLMER -
D. SONDERMANN,
Hedging of nonredundant contingent claims, In:
Contributions to Mathematical Economics in Honor of Gérard Debreu,
W. Hildenbrand,
A. Mas-Colell, eds.
North Holland, Amsterdam,
1986, 205-223. |
MR 902885 |
Zbl 0663.90006[27]
H. FÖLLMER -
M. SCHWEIZER,
Hedging of contingent claims under incomplete information, In:
Applied Stochastic Analysis,
M. H. A. Davis,
R. J. Elliott, eds.
Gordon & Breach, London,
1991, 389-414. |
MR 1108430 |
Zbl 0738.90007[28]
M. FRITTELLI,
Introduction to a theory of value coherent with the no-arbitrage principle,
Finance and Stochastics,
4(
2000), 275-297. |
fulltext (doi) |
MR 1779580[29]
M. FRITTELLI -
P. LAKNER,
Almost sure characterization of martingales,
Stochastics and Stochastics Reports,
49(
1994), 181-190. |
MR 1785004 |
Zbl 0827.60032[31]
J. M. HARRISON -
D. M. KREPS,
Martingales and arbitrage in multiperiod securities markets,
Journal of Economic Theory,
20(
1979), 381-408. |
fulltext (doi) |
MR 540823 |
Zbl 0431.90019[32]
J. M. HARRISON -
S. R. PLISKA,
Martingales and stochastic integrals in the theory of continuous trading,
Stochastic Processes and Their Applications,
11(
1981), 215-260. |
fulltext (doi) |
MR 622165 |
Zbl 0482.60097[33]
J. M. HARRISON -
S. R. PLISKA,
A stochastic calculus model of continuous trading: completemarkets,
Stochastic Processes and Their Applications,
15 (
1983), 313-316. |
fulltext (doi) |
MR 711188 |
Zbl 0511.60094[34] J. HULL - A. WHITE, The pricing of options with stochastic volatilities, Journal of Finance, 42(1987), 281-300.
[36]
I. KARATZAS -
J. LEHOCZKY -
S. E. SHREVE,
Optimal portfolio and consumption decisions for a small investor on a finite horizon,
SIAM J. on Control and Optimiz.,
25(
1987), 1557-1586. |
fulltext (doi) |
MR 912456 |
Zbl 0644.93066[37]
R. KORN,
Optimal portfolios: stochastic models for optimal investment and risk management in continuous time,
World Scientific, Singapore
1997. |
Zbl 0931.91017[38] J. LINTNER, The valuation of risky assets and the selection of risky investments instock portfolios and capital budgets, Review of Economics and Statistics, 47(1965), 13-37.
[39]
M. J. P. MAGILL -
G. M. COSTANTINIDES,
Portfolio selection with transaction costs,
Journal of Economic Theory,
13(
1976), 245-263. |
MR 469196 |
Zbl 0361.90001[40] B. MANDELBROT, The variation of certain speculative prices, Journal of Business, 36(1963), 394-419.
[41]
B. MANDELBROT,
Fractals and scaling in finance: discontinuity, concentration, risk,
Springer 1997. |
MR 1475217 |
Zbl 1005.91001[42]
R. N. MANTEGNA -
H. E. STANLEY,
An introduction to Econophysics: correlation and complexity in finance,
Cambridge University Press,
2000. |
MR 2343447 |
Zbl 0935.91023[43] H. M. MARKOWITZ, Portfolio selection, Journal of Finance, 7 (1952), 77-91.
[44]
F. MERCURIO -
W. J. RUNGGALDIER,
Option pricing for jump-diffusions: approximations and their interpretation,
Mathematical Finance,
3(
1993), 191-200. |
Zbl 0884.90043[45]
R. C. MERTON,
An intertemporal capital asset pricing model,
Econometrica,
41(
1973), 867-887. |
MR 441271 |
Zbl 0283.90003[46]
R. C. MERTON,
Option pricing when underlying stock returns are discontinuous,
Journal of Financial Economics,
3(
1976), 125-144. |
Zbl 1131.91344[47] J. MOSSIN, Equilibrium in a capital asset market, Econometrica, 3 (1966), 768-783.
[48]
S. MULINACCI,
An approximation of American option prices in a jump-diffusion model,
Stochastic Processes and Their Applications,
62 (
1996), 1-17. |
fulltext (doi) |
MR 1388760 |
Zbl 0848.90005[49]
S. A. ROSS,
The arbitrage theory of capital asset pricing,
Journal of Economic Theory,
13(
1976), 341-360. |
MR 429063[50] W. E. SHARPE, A simplified model of portfolio analysis, Management Science, 9(1963), 277-293.
[51] W. E. SHARPE, Capital asset prices: A theory of market equilibrium under conditions of risk, Journal of Finance, 19(1964), 425-442.
[52] S. M. SUNDARESAN, Continuous-Time Methods in Finance: A Review and an Assessment, Journal of Finance, 55(2000), 1569-1622.
[53]
M. S. TAQQU,
Bachelier and his Times: A Conversation with Bernard Bru,
Finance and Stochastics,
5(
2001). |
fulltext (doi) |
MR 1807874[54]
J. VONNEUMANN -
O. MORGENSTERN,
Theory of Games and Economic Behaviour,
Princeton University Press 1944. |
MR 11937 |
Zbl 0053.09303
Con il contributo del Ministero per i Beni e le Attività Culturali