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L^p Solutions of Backward Stochastic Volterra Integral Equations 被引量：1

L^p Solutions of Backward Stochastic Volterra Integral Equations
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摘要 This paper is devoted to the unique solvability of backward stochastic Volterra integral equations （BSVIEs, for short）, in terms of both M-solution and the adapted solutions. We prove the existence and uniqueness of M-solutions of BSVIEs in Lp （1 〈 p 〈 2）, which extends the existing results on M-solutions. The unique solvability of adapted solutions of BSVIEs in Lp （p 〉 1） is also considered, which also generalizes the results in the existing literature. This paper is devoted to the unique solvability of backward stochastic Volterra integral equations （BSVIEs, for short）, in terms of both M-solution and the adapted solutions. We prove the existence and uniqueness of M-solutions of BSVIEs in Lp （1 〈 p 〈 2）, which extends the existing results on M-solutions. The unique solvability of adapted solutions of BSVIEs in Lp （p 〉 1） is also considered, which also generalizes the results in the existing literature.
作者 Tian Xiao WANG
机构地区 School of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第9期1875-1882,共8页 数学学报（英文版）
基金 Supported in part by National Natural Science Foundation of China (Grant Nos. 10771122 and 11071145) Natural Science Foundation of Shandong Province of China (Grant No. Y2006A08) Foundation for Innovative Research Groups of National Natural Science Foundation of China (Grant No. 10921101) National Basic Research Program of China (973 Program, Grant No. 2007CB814900) Independent Innovation Foundation of Shandong University (Grant No. 2010JQ010) Graduate Independent Innovation Foundation of Shandong University (GIIFSDU)
关键词 Backward stochastic Volterra integral equations M-solutions Lp solutions adapted solutions Backward stochastic Volterra integral equations, M-solutions, Lp solutions, adapted solutions
分类号 O211.63 [理学—概率论与数理统计]
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参考文献14

  • 1Lin, J.: Adapted solution of backward stochastic nonlinear Volterra integral equation. Stoch. Anal. Appl., 20, 165-183 (2002).
  • 2Yong, J.: Backward stochastic Volterra integral equations and some related problems. Stoch. Proc. Appl., 116, 779-795 (2006).
  • 3Yong, J.: Well-posedness and regularity of backward stochastic Volterra integral equation. Probab. Theory Relat. Fields, 142, 21-77 (2008).
  • 4Wang, T., Shi, Y.: Symmetrical solutions of backward stochastic Volterra integral equations and applica- tions. Discrete Contin. Dyn. Syst. B, 14, 251-274 (2010).
  • 5Pardoux, E., Peng, S.: Adapted solution of a backward stochastic differential equation. Syst. Control. Lett., 14, 55-61 (1990).
  • 6Yong, J.: Continuous-time dynamic risk measures by backward stochastic Volterra integral equations. Appl. Anal., 86, 1429-1442 (2007).
  • 7Rosazza, E.: Risk measures via g-expectation. Insur. Math. Econ., 39, 19-34 (2006).
  • 8Wang, Z., Zhang, X.: Non-Lipschitz backward stochastic Volterra integral equations with jumps. S$och. Dyn,, 7, 479-496 (2007).
  • 9ren, Y.: On solutions of backward stochastic Volterra integral equations with jumps in Hilbert spaces. J Optim. Theory Appl., 144, 319-333 (2010).
  • 10El Karoui, N., Peng, S., Quenez, M.: Backward stochastic differential equations in finance. Math. Finance, 7, 1-71 (1997).

同被引文献29

  • 1A. Aman and M. N'Zi. Backward stochastic nonlinear integral equation with local Lipschitz drift, Probab Math Statist, 2005, 25: 105-127.
  • 2V. Anh and J. Yong. Backward stochastic Volte~ra integral equations in Hilbert space, Differential Difference Equations Appl, Hindawi, New York, 2006, 57-66.
  • 3F. Antonelli. Backward-forward stochastic differential equations, Ann Appl Probab, 1993, 3: 777- 793.
  • 4M. Berger and V. Mizel. VoIterra equation with It5 integrals, I, II, J Intergal Equations, 1980, 2: 187-245, and 319-337.
  • 5J. M. Bismut. Th@orie Probabiliste du Contr51e des Diffusions, Mere Amer Math Soc, 176, Provi- dence, Rhode Island, 1973.
  • 6V. G. Boltyanskii, R. V. Gamkrelidze, and L. S. Pontryagin. On the theory of optimal processes, Dokl Akad Nauk SSSR (N.S.), 1956, 110:7-10 (in Russian).
  • 7Ph. Briand, B. Delyon, Y. Hu, E. Pardoux, and L. Stoica. Lp solutions of backward stochastic differential equations, Stochastic Process Appl, 2003, 108: 109-129.
  • 8D. Duffie and L. Epstein. Stochastic differential utility, Econometrica, 1992, 60: 353-394.
  • 9D. Duffle and C. F. Huang. Stochastic production-exchange equilibria, Research paper No. 974 Graduate School of Business, Stanford Univ, 1986.
  • 10N. E1 Karoui, S. Peng, and M. C. Quenez. backward stochastic differential equations in finance, Math Finance, 1997, 7: 1-71.

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Acta Mathematica Sinica,English Series
2012年 第9期

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