Numerical solution of portfolio optimal control with constraints: the case of the object as weakly singular integral equation

• Autorzy: Filatova D. , Grzywaczewski M.
• Języki publikacji: EN

Abstrakty

EN

We consider the model of optimal portfolio of Mertons’ market model. The noises involved in the dynamics of the wealth are fractional white noises. The stochastic optimal control problem is converted into a non-random optimization. An example of problem numerical solution illustrates proposed methodology.

Słowa kluczowe

EN

fractional Brownian motion; integral equations; probability

PL

równania całkowite; prawdopodobieństwo

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Journal of Applied Computer Science
• Rocznik: 2007
• Tom: Vol. 15, nr 2
• Strony: 51--69
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Filatova D.

autor

Grzywaczewski M.

• Radom Technical University Department of Mathematics ul. Malczewskiego 20A, 26600 Radom, Poland,

Bibliografia

• [1] Baratella P., Orsi A.P.: A new approach to the numerical solution of weakly singular Volterra integral equations, Journal of Computational and Applied Mathematics, 2004, Vol. 163, pp. 401 - 418.
• [2] Biagini F., Hu Y., Oksendal B., Sulem A.: A stochastic maximum principle for processes driven by fractional Brownian motion, Stochastic Processes and their Application, 2002, Vol. 100, pp. 233 - 253.
• [3] Bellman R.: Dynamic Programming, Princeton: Princeton Univ. Press., 1957.
• [4] Crandall M.G., Lions P.L.: Conditions d'unicite pour les solutions generalies des equations d'Hamilton-Jacobi du premier ordre, C.R. Acad. Sci. Paris Ser.I, Math., 1981, Vol. 292, pp. 487 - 502.
• [5] Filatova D., Grzywaczewski M., Zili. M.: Portfolio optimization problem of Mertons' market model driven by a fractional Brownian motion, Proceedings of the 33rd International Conference MACROMODELS 2006, Absolwent, Łódź, pp. 181 - 197.
• [6] Hosking J.R.M.: Fractional differencing. Biometrica, 1981, Vol. 68(1), pp. 165-176
• [7] Jumarie G.: Fractional Brownian motions via random walk in the complex plane and via fractional derivative. Comparison and further results on their Fokker- Planck equations, Chaos, Solutions and Fractals, 2004, Vol. 22, pp. 907 - 925.
• [8] Jumarie G. Merton's model of optimal portfolio in a Black-Scholes market driven by a fractional Brownian motion with short-range dependence, Insurance: Mathematics and Economics, 2005, Vol. 37, pp. 585 - 598.
• [9] Mandelbrot B.B. and van Ness J.W.: Fractional Brownian motions, fractional noises and applications, SIAM Review, vol. 10, pp. 422-437, 1968.
• [10] Merton R.C.: Lifetime portfolio selection under uncertainty: the continuous-time case, The Review of Economics and Statistics, 1969, vol. 51, pp. 247 - 257.
• [11] Merton R.C.: Optimal consumption and portfolio rules in a continuous-time model, Journal of Economic Theory, 1971, Vol. 3, pp. 373 - 413.
• [12] Monegato G., Scuderi L.: High order methods for weakly singular integral equations with nonsmoth input functions, Mathematical Computation, 1998, Vol. 67, pp. 1493 - 1515
• [13] Roussas G.: Introduction to probability and Statistical Inference. AP Elsevier Science, 2003, p. 523
• [14] Shyryaev A.N.: The basis of financial mathematics: facts, models. FAZIS, Moscow, 1998 (in Russian)