본문 바로가기
KERD
논문KCI 등재

MEAN-FIELD BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS ON MARKOV CHAINS

Wen Lu|Yong Ren
대한수학회 (The Korean Mathematical Society)|2017.01|대한수학회보 (Bulletin of the KMS)|제54권 제1호|pp. 17-28

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

Markov chaincomparison theorem
주제분류수학

초록

In this paper, we deal with a class of mean-field backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We obtain the existence and uniqueness theorem and a comparison theorem for solutions of one-dimensional mean-field BSDEs under Lipschitz condition.

Abstract

In this paper, we deal with a class of mean-field backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We obtain the existence and uniqueness theorem and a comparison theorem for solutions of one-dimensional mean-field BSDEs under Lipschitz condition.

참고문헌 (24)

  1. N. Ahmed, "Nonlinear diffusion governed by McKean-Vlasov equation on Hilbert space and optimal control", SIAM J. Control Optim, 46(1,), pp.356~378 (2007)
  2. N. Ahmed, "A semilinear McKean-Vlasov stochastic evolution equation in Hilbert space", Stochastic Process. Appl, 60(1), pp.65~85 (1995)
  3. V. Borkar, "McKean-Vlasov limit in portfolio optimization", Stoch. Anal. Appl, 28(5,), pp.884~906 (2010)
  4. R. Buckdahn, "Mean-field backward stochastic differential equations: a limit approach", Ann. Probab, 37(4), pp.1524~1565 (2009)
  5. R. Buckdahn, "Mean-field backward stochastic differential equations and related partial differential equations", Stoch. Process. Appl, 119(10), pp.3133~3154 (2009)
  6. T. Chan, "Dynamics of the McKean-Vlasov equation", Ann. Probab, 22(1), pp.431~441 (1994)
  7. S. N. Cohen, "Solutions of backward stochastic differential equations on Markov chains", Commun. Stoch. Anal, 2(2,), pp.251~262 (2008)
  8. S. N. Cohen, "Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions", Ann. Appl. Probab, 20(1), pp.267~311 (2010)
  9. S. N. Cohen, "Existence, uniqueness and comparisons for BSDEs in general spaces", Ann. Probab, 40(5), pp.2264~2297 (2012)
  10. D. Crisan, "Approximate McKean-Vlasov representations for a class of SPDEs", Stochastics, 82, pp.53~68 (2010)
  11. N. El Karoui, "Backward stochastic differential equations in finance", Math. Finance, 7(1), pp.1~71 (1997)
  12. R. J. Elliott, "Markov Models: Estimation and Control" (1994), Springer-Verlag
  13. S. Hamad`ene, "Zero-sum stochastic differential games and backward equations", Systems Control Lett, 24(4), pp.259~263 (1995)
  14. M. Kac, "Foundations of kinetic theory", Proceedings of the Third Berkeley Sympo-sium on Mathematical Statistics and Probability, 3, pp.171~197 (1956), Uni-versity of California Press
  15. P. Kotelenez, "A class of quasilinear stochastic partial differential equations of McKean-Vlasov type with mass conservation", Probab. Theory Related Fields, 102(2), pp.159~188 (1995)
  16. P. Kotelenez, "Macroscopic limit for stochastic partial differential equations of McKean-Vlasov type, Probab", Theory Related Fields, 146(1-2), pp.189~222 (2010)
  17. J. Lasry, "Mean field games", Jpn J. Math, 2(1), pp.229~260 (2007)
  18. J. Li, "Reflected Mean-Field Backward Stochastic Differential Equations, Approximation and Associated Nonlinear PDEs", J. Math. Anal. Appl, 413(1), pp.47~68 (2014)
  19. Z. Li, "Mean-field reflected backward stochastic differential equations", Statist. Probab. Lett, 82(11), pp.1961~1968 (2012)
  20. W. Lu, "Anticipated backward stochastic differential equations on Markov chains", Statist. Probab. Lett, 83(7), pp.1711~1719 (2013)
  21. H. McKean, "A class of Markov processes associated with nonlinear parabolic equations", Proc. Nat. Acad. Sci. U.S.A, 56, pp.1907~1911 (1966)
  22. E. Pardoux, "Adapted solution of a backward stochastic differential equation", Systems Control Lett, 14(1), pp.55~61 (1990)
  23. S. Peng, "Backward stochastic differential equations and applications to optimal control", Appl. Math. Optim, 27(2), pp.125~144 (1993)
  24. R. Xu, "Mean-field backward doubly stochastic differential equations and related SPDEs", Bound. Value Probl, (114), pp.20~ (2012)

관련 논문AI추천

$\mathbb{D}$-solutions of BSDEs with Poisson jumpsImen Hassairi대한수학회 · 대한수학회지2022 · 제59권 제6호BSDEs on finite and infinite time horizon with discontinuous coefficientsPengju Duan, Yong Ren대한수학회 · 대한수학회보2013 · 제50권 제4호$L^p$-solutions for reflected BSDEs with time delayed generatorsQing Zhou대한수학회 · 대한수학회보2016 · 제53권 제3호Solvability of general backward stochastic Volterra integral equationsTianxiao Wang, Yufeng Shi대한수학회 · 대한수학회지2012 · 제49권 제6호$L^p$ solutions for general time interval multidimensional BSDEs with weak monotonicity and general growth generatorsShengjun Fan, Yongpeng Dong대한수학회 · 대한수학회논문집2018 · 제33권 제3호Lp (p ≥ 1) SOLUTIONS OF MULTIDIMENSIONAL BSDES WITH TIME-VARYING QUASI-HOLDER CONTINUITY GENERATORS IN GENERAL TIME INTERVALSFAN Sheng-Jun, Xiao Lishun대한수학회 · 대한수학회논문집2020 · 제35권 제2호

이 간행물의 다른 논문 (24건)

A recursive formula for the Khovanov cohomology of Kanenobu knotsFengchun Lei, Meili Zhangpp. 1-15New extremal binary self-dual codes of lengths 66 and 68 from codes over Rk,mNesibe Tufekci, Abidin Kayapp. 29-42The height of a class of ternary cyclotomic polynomialsBin Zhangpp. 43-50On commutativity of skew polynomials at zeroFatma Kaynarca, Hai Lan Jin, 이양, 곽태근pp. 51-69Qualitative uncertainty principle for Gabor transformAjay Kumar, Ashish Bansalpp. 71-84
원문 보기