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Stochastic integral with respect to set-valued square integrable martingales |
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| Authors: | Shoumei Li Xiaohua Li |
| Institution: | a Department of Applied Mathematics, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing 100124, PR China b Mainbo Education, Science and Technology Company, B 1507, 3 Danling Street, Haidian District, Beijing 100080, PR China c School of Science, Beijing University of Posts and Telecommunications, 10 Xitucheng, Haidian District, Beijing 100876, PR China |
| Abstract: | In this paper, we shall firstly illustrate why we should consider integral of a stochastic process with respect to a set-valued square integrable martingale. Secondly, we shall prove the representation theorem of set-valued square integrable martingale. Thirdly, we shall give the definition of stochastic integral of a stochastic process with respect to a set-valued square integrable martingale and the representation theorem of this kind of integrals. Finally, we shall prove that the stochastic integral is a set-valued sub-martingale. |
| Keywords: | Set-valued square integrable martingale Set-valued stochastic integral Representation theorem |
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