Abstract:
This paper can be viewed as an introduction to the papers of this issue devoted to some theoretical-probabilistic problems in financial mathematics. In this paper, we describe key structures of finance theory (§ 1), present a brief historical bibliography (§ 2), and consider (§ 3) stochastic models of a stock exchange. In addition, the paper offers an insight into the problems of option pricing (§ 4).
Keywords:
finance theory, financial mathematics, stock exchange models, bond and stock, options, warrants, futures contracts.
Citation:
A. N. Shiryaev, “On some basic concepts and some basic stochastic models used in finance”, Teor. Veroyatnost. i Primenen., 39:1 (1994), 5–22; Theory Probab. Appl., 39:1 (1994), 1–13
G. L. Bukhbinder, K. M. Chistilin, “Opisanie rossiiskogo fondovogo rynka v ramkakh modeli Gestona”, Matem. modelirovanie, 17:10 (2005), 31–38
I. Kolmanovsky, T.L. Maizenberg, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301), 2002, 4250
O. V. Shataev, “Minimization with respect to entropy in the problem of finding a martingale measure”, Russian Math. Surveys, 55:5 (2000), 1000–1002
Carl J. G. Evertsz, Ralf Hendrych, Peter Singer, Heinz-Otto Peitgen, Komplexe Systeme und Nichtlineare Dynamik in Natur und Gesellschaft, 1999, 400
O. V. Shataev, “On a fair price of an option of European type”, Russian Math. Surveys, 53:6 (1998), 1367–1369
A. V. Melnikov, “Stochastic differential equations: singularity of coefficients, regression models, and stochastic approximation”, Russian Math. Surveys, 51:5 (1996), 819–909
L. A. Shepp, A. N. Shiryaev, “A new look at pricing of the “Russian Option””, Theory Probab. Appl., 39:1 (1994), 103–119
A. N. Shiryaev, Yu. M. Kabanov, D. O. Kramkov, A. V. Melnikov, “Toward the theory of pricing of options of both European and American types. I. Discrete time”, Theory Probab. Appl., 39:1 (1994), 14–60
D. O. Kramkov, É. Mordecki, “Integral option”, Theory Probab. Appl., 39:1 (1994), 162–172
A. N. Shiryaev, Yu. M. Kabanov, D. O. Kramkov, A. V. Melnikov, “Toward the theory of pricing of options of both European and American types. II. Continuous time”, Theory Probab. Appl., 39:1 (1994), 61–102
S. T. Rachev, L. Rüscheendorf, “Models for option prices”, Theory Probab. Appl., 39:1 (1994), 120–152
Citation in format AMSBIB
Contact us: