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.
@article{BUMI_1999_8_2A_3_297_0,
author = {Wolfgang J. Runggaldier},
title = {Sugli sviluppi della matematica applicata in un settore interdisciplinare: la finanza matematica},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {2-A},
year = {1999},
pages = {297-316},
zbl = {05292608},
mrnumber = {1832863},
language = {it},
url = {http://dml.mathdoc.fr/item/BUMI_1999_8_2A_3_297_0}
}
Runggaldier, Wolfgang J. Sugli sviluppi della matematica applicata in un settore interdisciplinare: la finanza matematica. Bollettino dell'Unione Matematica Italiana, Tome 2-A (1999) pp. 297-316. http://gdmltest.u-ga.fr/item/BUMI_1999_8_2A_3_297_0/
[1] AAVV, Atti del Convegno Ricordo di Bruno de Finetti Professore nell’Ateneo triestino, Dipartimento di Matematica Applicata «Bruno de Finetti», Trieste, 1987.
[2] - - - , Coherent measures of risk, Mathematical Finance, 9(1999), 203-228. | MR 1850791 | Zbl 0980.91042
[3] - , Existence of an equilibrium for a competitive economy, Econometrica, 22(1954), 265-290. | MR 77069 | Zbl 0055.38007
[4] , Théorie de la spéculation, Gauthier-Villars1900. Anche in: Annales Scientifiques de l’École Normale Supérieure, 1900, 21-86. | JFM 31.0241.02
[5] , Equazioni differenziali stocastiche e applicazioni, Quaderni UMI Vol. 28, Pitagora, Bologna, 1984. | Zbl 0606.60051
[6] , Exposition of a new theory on the measurement of risk, trad. di in Econometrica, 22(1954), 23-36. | MR 59834 | Zbl 0055.12004
[7] - , Risk sensitive asset management with transaction costs, Finance and Stochastics, 4(2000), 1-33. | MR 1790132
[8] - - - , Towards a general theory of bond markets, Finance and Stochastics, 1(1997), 141-174. | Zbl 0889.90019
[9] - , The pricing of options and corporate liabilities, Journal of Political Economy, 81(1973), 637-654. | Zbl 1092.91524
[10] , Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31(1986), 307-327. | MR 853051 | Zbl 0616.62119
[11] - , Criteri per la selezione del portafoglio, G. Giappichelli, Torino, 1991.
[12] - , Introduzione alla selezione di portafoglio, Cooperativa di Cultura «Lorenzo Milani», Torino, 1991.
[13] - - - , Louis Bachelier on the centenary of Théorie de la Spéculation, Mathematical Finance, 10 (2000), 341-353. | MR 1800320
[14] - - , Option pricing: a simplified approach, Journal of Financial Economics, 7(1979), 229-263. | Zbl 1131.91333
[15] - , On dynamic measures of risk, Finance and Stochastics, 3(1999), 451-482. | MR 1842283 | Zbl 0982.91030
[16] - - , A closed-form solution to the problem of super-replication under transaction costs, Finance and Stochastics, 3 (1999), 35-54. | Zbl 0924.90010
[17] - - , Equivalent martingale measures and no-arbitrage in stochastic securities market models, Stochastics and Stochastic Reports, 29(1990), 185-201. | MR 1041035 | Zbl 0694.90037
[18] - , Portfolio selection with transaction costs, Mathematics of Operations Research, 15(1990), 676-713. | MR 1080472 | Zbl 0717.90007
[19] - , A general version of the fundamental theorem of asset pricing, Mathematische Annalen, 300(1994), 463-520. | MR 1304434 | Zbl 0865.90014
[20] - , Three centuries of asset pricing, London Business School, Institute of Finance & Accounting WP-295, Jan 2000.
[21] - , A yield factor model of interest rates, Mathematical Finance, 6(1966), 379-406. | Zbl 0915.90014
[22] - , Dynamic programming and pricing of contingent claimsin an incomplete market, SIAM J. on Control and Optimiz., 33(1995), 29-66. | MR 1311659 | Zbl 0831.90010
[23] , Autoregressive conditional heteroskedasticity with estimates of the variance of UK inflation, Econometrica, 50(1982), 987-1007. | MR 666121 | Zbl 0491.62099
[24] , The behaviour of stock market prices, Journal of Business, 38 (1965), 34-105.
[25] - , Efficient hedging: cost versus shortfall risk, Finance and Stochastics, 4(2000), 117-146. | MR 1780323
[26] - , Hedging of nonredundant contingent claims, In: Contributions to Mathematical Economics in Honor of Gérard Debreu, , , eds. North Holland, Amsterdam, 1986, 205-223. | MR 902885 | Zbl 0663.90006
[27] - , Hedging of contingent claims under incomplete information, In: Applied Stochastic Analysis, , , eds. Gordon & Breach, London, 1991, 389-414. | MR 1108430 | Zbl 0738.90007
[28] , Introduction to a theory of value coherent with the no-arbitrage principle, Finance and Stochastics, 4(2000), 275-297. | MR 1779580
[29] - , Almost sure characterization of martingales, Stochastics and Stochastics Reports, 49(1994), 181-190. | MR 1785004 | Zbl 0827.60032
[30] , ARCH models and financial applications, Springer, 1997. | MR 1439744 | Zbl 0880.62107
[31] - , Martingales and arbitrage in multiperiod securities markets, Journal of Economic Theory, 20(1979), 381-408. | MR 540823 | Zbl 0431.90019
[32] - , Martingales and stochastic integrals in the theory of continuous trading, Stochastic Processes and Their Applications, 11(1981), 215-260. | MR 622165 | Zbl 0482.60097
[33] - , A stochastic calculus model of continuous trading: completemarkets, Stochastic Processes and Their Applications, 15 (1983), 313-316. | MR 711188 | Zbl 0511.60094
[34] - , The pricing of options with stochastic volatilities, Journal of Finance, 42(1987), 281-300.
[35] , Optimization problems in the theory of continuous trading, SIAM J. on Control and Optimiz., 27(1989), 1221-1259. | MR 1022426 | Zbl 0701.90008
[36] - - , Optimal portfolio and consumption decisions for a small investor on a finite horizon, SIAM J. on Control and Optimiz., 25(1987), 1557-1586. | MR 912456 | Zbl 0644.93066
[37] , Optimal portfolios: stochastic models for optimal investment and risk management in continuous time, World Scientific, Singapore1997. | Zbl 0931.91017
[38] , 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] - , Portfolio selection with transaction costs, Journal of Economic Theory, 13(1976), 245-263. | MR 469196 | Zbl 0361.90001
[40] , The variation of certain speculative prices, Journal of Business, 36(1963), 394-419.
[41] , Fractals and scaling in finance: discontinuity, concentration, risk, Springer1997. | MR 1475217 | Zbl 1005.91001
[42] - , An introduction to Econophysics: correlation and complexity in finance, Cambridge University Press, 2000. | MR 2343447 | Zbl 0935.91023
[43] , Portfolio selection, Journal of Finance, 7 (1952), 77-91.
[44] - , Option pricing for jump-diffusions: approximations and their interpretation, Mathematical Finance, 3(1993), 191-200. | Zbl 0884.90043
[45] , An intertemporal capital asset pricing model, Econometrica, 41(1973), 867-887. | MR 441271 | Zbl 0283.90003
[46] , Option pricing when underlying stock returns are discontinuous, Journal of Financial Economics, 3(1976), 125-144. | Zbl 1131.91344
[47] , Equilibrium in a capital asset market, Econometrica, 3 (1966), 768-783.
[48] , An approximation of American option prices in a jump-diffusion model, Stochastic Processes and Their Applications, 62 (1996), 1-17. | MR 1388760 | Zbl 0848.90005
[49] , The arbitrage theory of capital asset pricing, Journal of Economic Theory, 13(1976), 341-360. | MR 429063
[50] , A simplified model of portfolio analysis, Management Science, 9(1963), 277-293.
[51] , Capital asset prices: A theory of market equilibrium under conditions of risk, Journal of Finance, 19(1964), 425-442.
[52] , Continuous-Time Methods in Finance: A Review and an Assessment, Journal of Finance, 55(2000), 1569-1622.
[53] , Bachelier and his Times: A Conversation with Bernard Bru, Finance and Stochastics, 5(2001). | MR 1807874
[54] - , Theory of Games and Economic Behaviour, Princeton University Press 1944. | MR 11937 | Zbl 0053.09303