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2006 | 26 | 1 | 83-103
Tytuł artykułu

Properties of set-valued stochastic integrals

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We introduce set-valued stochastic integrals driven by a square-integrable martingale and by a semimartingale. We investigate properties of both integrals.
Twórcy
autor
  • Faculty of Mathematics, Computer Science and Econometrics University of Zielona Góra Szafrana 4a, 65-516 Zielona Góra, Poland
autor
  • Faculty of Mathematics, Computer Science and Econometrics University of Zielona Góra Szafrana 4a, 65-516 Zielona Góra, Poland
Bibliografia
  • [1] K.K. Aase and P. Guttrup, Estimation in models for security prices, Scand. Actuarial J. 3/4 (1987), 211-225.
  • [2] J.P. Aubin and H. Frankowska, Set-valued analysis, Birkhäuser Boston-Basel-Berlin 1990.
  • [3] G. Boscan, On Wiener stochastic integral of a multifunction, Seminarul de Teoria Probabilitatilor si Applicatii, Univ. Timisoara 1987.
  • [4] C. Castaing, Sur les multi-applications measurables, Rev. Fr. Inf. Recher. Oper. 1 (1967), 91-126.
  • [5] K.L. Chung and R.J. Williams, Introduction to stochastic integration, Birkhäuser Boston-Basel-Berlin 1990.
  • [6] D. Duffie, Dynamic Asset Pricing Theory, Princeton Univ. Press, Princeton, New Jersey 1996.
  • [7] E. Eberlein and U. Keller, Hyperbolic distributions in finance, Bernoulli 1 (1995), 281-299.
  • [8] B.D. Gelman and J.S. Gliklikh, Set-valued Itô integral, Priblizennye Metody Issledovani Differentialnych Uravneni i ikh Prilozeni, Mezbuzovskii Sbornik, Kuibyshevskii Universitaet (1984) (in Russian).
  • [9] I.I. Gihman and A.V. Skorohod, Stochastic Differential Equations, Springer Verlag, Berlin-Heidelberg-New York 1972.
  • [10] F. Hiai and H. Umegaki, Integrals, conditional expectations and martingales of multivalued functions, J. Multivar. Anal. 7 (1977), 149-182.
  • [11] F. Hiai, Multivalued stochastic integrals and stochastic differential inclusions, Division of Applied Mathematics, Research Institude of Applied Electricity, Sapporo 060, Japan, (not published).
  • [12] M. Kisielewicz, Set-valued Stochastic Integrals and Stochastic Inclusions, Stoch. Anal. Appl. 15 (5) (1997), 783-800.
  • [13] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer Acad. Publ. and Polish Sci. Publ., Warszawa-Dordrecht-Boston-London 1991.
  • [14] M. Kisielewicz, M. Michta and J. Motyl, Set Valued Approach to Stochastic Control. Part I (Existence and regurality properties), Dynamic Syst. Appl. 12 (3) (2003), 405-432.
  • [15] M. Kisielewicz, M. Michta and J. Motyl, Set Valued Approach to Stochastic Control. Part II (Viability and Semimartingale Issues), Dynamic Syst. and Appl. 12 (3) (2003), 433-466.
  • [16] P. Protter, Stochastic Integration and Differential Equations (A New Approach), Springer-Verlag, Berlin-Heideberg-New York 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1076
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