PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Powiadomienia systemowe
  • Sesja wygasła!
Tytuł artykułu

A time-changed stochastic control problem and its maximum principle

Autorzy
Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper studies a time-changed stochastic control problem, where the underlying stochastic process is a Lévy noise time-changed by an inverse subordinator. We establish a maximum principle for the time-changed stochastic control problem. We also prove the existence and uniqueness of the corresponding time-changed backward stochastic differ- ential equation involved in the stochastic control problem. Some examples are provided for illustration.
Rocznik
Strony
193--215
Opis fizyczny
Bibliogr.17 poz., wykr.
Twórcy
autor
  • Auburn University 221 Parker Hall Auburn, AL 36849, U.S.A
autor
  • Lewis University One University Parkway Romeoville, IL 60446, U.S.A
Bibliografia
  • [1] A. Bensoussan, Maximum principle and dynamic programming approaches to the optimal control of partially observed diffusions, Stochastics 9 (1983), 169-222.
  • [2] J. M. Bismut, Conjugate convex functions in optimal stochastic control, J. Math. Anal. Appl. 44 (1973), 384-404.
  • [3] W. H. Fleming and T. Pang, An application of stochastic control theory to financial economics, SIAM J. Control 43 (2004), 502-531.
  • [4] N. C. Framstad, B. Øksendal and A. Sulem, Sufficient stochastic maximum principle for the optimal control of jump diffusions and applications to finance, J. Optim. Theory Appl. 124 (2005), 511–512.
  • [5] J. Janczura and A. Wyłoma ́nska, Subdynamics of financial data from fractional Fokker-Planck equation, Acta Phys. Polon. B 40 (2009), 1341-1351.
  • [6] M. Hahn, K. Kobayashi and S. Umarov, SDEs driven by a time-changed Lévy process and their associated time-fractional order pseudo-differential equations, J. Theoret. Probab. 25 (2012), 262-279.
  • [7] E. Jum and K. Kobayashi, A strong and weak approximation scheme for stochastic differentia equations driven by a time-changed Brownian motion, Probab. Math. Statist. 36 (2016), 201-220.
  • [8] H. J. Kushner, Necessary conditions for continuous parameter stochastic optimization problems, SIAM J. Control 10 (1972), 550-565.
  • [9] M. Magdziarz and T. Zorawik, Stochastic representation of a fractional subdiffusion equation. The case of infinitely divisible waiting times, Lévy noise and space-time-dependent coefficients, Proc. Amer. Math. Soc. 144 (2016), 1767-1778.
  • [10] M. M. Meerschaert and P. Straka, Inverse stable subordinators, Math. Model. Nat. Phenom. 8 (2013), no. 2, 1-16.
  • [11] E. Nane and Y. Ni, Path stability of stochastic differential equations driven by time-changed Lévy noises, ALEA Latin Amer. J. Probab. Math. Statist. 15 (2018), 479-507.
  • [12] E. Nane and Y. Ni, Stability of the solution of stochastic differential equation driven by time-changed Lévy noise, Proc. Amer. Math. Soc. 145 (2017), 3085-3104.
  • [13] E. Nane and Y. Ni, Stochastic solution of fractional Fokker-Planck equations with space-time-dependent coefficients, J. Math. Anal. Appl. 442 (2016), 103-116.
  • [14] S. G. Peng, A general stochastic maximum principle for optimal control problems, SIAM J. Control Optim. 28 (1990), 966-979.
  • [15] W. J. Runggaldier, On stochastic control in finance, in: Mathematical Systems Theory in Biology, Communications, Computation, and Finance, Springer, New York, 2003, 317-344.
  • [16] D. Wilkinson, Stochastic Modelling for Systems Biology, Chapman and Hall/CRC, New York, 2006.
  • [17] Q. Wu, Stability analysis for a class of nonlinear time-changed systems, Cogent Math. 3 (2016), art. 1228273, 10 pp.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-f0dcf9e6-3b4d-4ea9-9890-f65c8f95d6d4
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.