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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