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Essays in Honour of Jia-an Yan
Editors
Tusheng ZhangUniversity of Manchester, UK
Xunyu Zhou
University of Oxford, UK
UK.
World Scientific
NEW JERSEY • LONDON • SINGAPORE . BEIJING • SHANGHAI • HONS KONG . TAIPEI • CHENNAt
Contents
Editorial Foreword Vll
A Biographical Note and Tribute to Jia-An Yan On His 70th Birthday IX
1. Non-linear evolution equations driven by rough paths 1
Thomas Cass, Zhongmin Qian and Jan Tudor
2. Optimal stopping times with different information levels and with time
uncertainty 19
Arijit Chakrabarty and Xin Guo
3. Finite horizon optimal investment and consumption with CARA
utility and proportional transaction costs 39
Ytngshan Chen, Min Dai and Kun Zhao
4. Uniform integrability of exponential martingales and spectral bounds
of non-local Feynman-Kac semigroups 55
Zhen-Qing Chen
5. Continuous-time mean-variance portfolio selection with finite transactions 77
Xiangyu Cui, Jianjun Gao and Duan Li
6. Quantifying model uncertainties in the space of probability measures 99
J. Duan, T. Gao and G. He
XI
xii Contents
7. A PDE approach to multivariate risk theory
Robert J. Elliott, Tak Kuen Siu and Hailiang Yang
111
8. Stochastic analysis on loop groups
Shizan Fang
125
9. Existence and stability of measure solutions for BSDE with generators
of quadratic growth
Alexander Fromm, Peter Imkeller and Jianing Zhang
137
10. Convex capital requirements for large portfolios 169
Hans Follmer and Thomas Knispel
11. The mixed equilibrium of insider trading in the market with rational
expected price 197
Fuzhou Gong and Hong Liu
12. Some results on backward stochastic differential equations driven by
fractional Brownian motions 225
Yaozhong Hu, Daniel Ocone and Man Song
13. Potential theory of subordinate Brownian motions revisited 243
Panki Kim, Renming Song and Zoran Vondracek
14. Research on social causes of the financial crisis 291
Steven Kou
15. Wick formulas and inequalities for the quaternion Gaussian and /3-
permanental variables 303
Wenbo V. Li and Ang Wei
16. Further study on web Markov skeleton processes 313
Yuting Liu, Zhi-Ming Ma and Chuan Zhou
17. MLE of parameters in the drifted Brownian motion and its error 341
Lemee Nakamura and Weian Zheng
Contents xiii
18. Optimal partial information control of SPDEs with delay and time-
advanced backward SPDEs 355
Bernt 0ksendal, Agnes Sulem and Tusheng Zhang
19. Simulation of diversified portfolios in continuous financial markets 385
Eckhard Platen and Renata Rendek
20. Coupling and applications 411
Feng-Yu Wang
21. SDEs and a generalised Burgers equation 425
Jiang-Lun Wu and Wei Yang
22. Mean-variance hedging in the discontinuous case 437
Jianming Xia