Stochastic analysis and applications to finance : essays in honour of Jia-an Yan / editors Tusheng Zhang, Xunyu Zhou.

Format:

Book

Contributor:

Zhang, Tusheng, 1963-

Zhou, Xun Yu.

Series:

Interdisciplinary Mathematical Sciences

Interdisciplinary Mathematical Sciences ; 13

Language:

English

Subjects (All):

Stochastic analysis.

Stochastic processes.

Stochastic systems.

Physical Description:

1 online resource (465 p.)

Place of Publication:

Singapore ; Hackensack, NJ : World Scientific, 2012.

Language Note:

English

Summary:

This volume is a collection of solicited and refereed articles from distinguished researchers across the field of stochastic analysis and its application to finance. The articles represent new directions and newest developments in this exciting and fast growing area. The covered topics range from Markov processes, backward stochastic differential equations, stochastic partial differential equations, stochastic control, potential theory, functional inequalities, optimal stopping, portfolio selection, to risk measure and risk theory. It will be a very useful book for young researchers who want t

Contents:

Editorial Foreword; A Biographical Note and Tribute to Jia-An Yan On His 70th Birthday; Contents; 1. Non-linear evolution equations driven by rough paths Thomas Cass, Zhongmin Qian and Jan Tudor; 1.1. Introduction; 1.2. Preliminaries; 1.3. Initial Estimates; 1.4. The Bochner Integral; 1.5. The Young Integral; 1.6. The Non-Linear Mapping L; 1.7. Randomly Forced Navier-Stokes Equations; Acknowledgement; References; 2. Optimal stopping times with different information levels and with time uncertainty Arijit Chakrabarty and Xin Guo; 2.1. Introduction; 2.1.1. Two Problems: A and B

2.1.2. Main results and analysis2.2. Mathematical Setup and Preliminaries; 2.3. Problem A: Relation between Two optimal Stopping Times with Time Uncertainty; 2.4. Problem B: Further Analysis; 2.4.1. Problem B: a motivating example; 2.4.2. Problem B: connectivity of the continuation region C; 2.4.2.1. When g is C2; 2.4.2.2. When g is the difference of two convex functions; 2.4.3. Examples: re-derivation of explicit solutions; References; 3. Finite horizon optimal investment and consumption with CARA utility and proportional transaction costs Yingshan Chen, Min Dai and Kun Zhao

3.1. Introduction3.2. Problem formulation; 3.3. Optimal strategy with transaction costs; 3.3.1. Optimal investment strategy; 3.3.2. Optimal consumption strategy; 3.4. Comparison between the consumption case and the no-consumption case; 3.5. Conclusion; References; 4. Uniform integrability of exponential martingales and spectral bounds of non-local Feynman-Kac semigroups Zhen-Qing Chen; 4.1. Introduction; 4.2. Kato classes and non-local Feynman-Kac transform; 4.3. Uniform integrability of exponential martingales; 4.4. Spectral bounds for local Feynman-Kac semigroup

4.5. Spectral bounds for non-local Feynman-Kac semigroupsAcknowledgement; References; 5. Continuous-time mean-variance portfolio selection with finite transactions Xiangyu Cui, Jianjun Gao and Duan Li; 5.1. Introduction; 5.2. Mean-variance portfolio selection without riskless asset; 5.3. When a riskless asset is included; 5.4. Mean-variance portfolio selection with finite transactions; 5.5. Conclusion and Discussion; A.1. The proof of Theorem 5.1; A.2. The proof of Theorem 5.2; References; 6. Quantifying model uncertainties in the space of probability measures J. Duan, T. Gao and G. He

6.1. Introduction6.1.1. Quantifying uncertainty in the space of paths; 6.1.2. Quantifying uncertainty in the space of probability measures; 6.1.3. Observation of stationary probability distributions; 6.1.4. Observation of time-dependent probability distributions; Acknowledgements; References; 7. A PDE approach to multivariate risk theory Robert J. Elliott, Tak Kuen Siu and Hailiang Yang; 7.1. Introduction; 7.2. Multivariate Ruin Theory; 7.2.1. A Single Line Risky Business; 7.2.2. Two Independent Lines of Risky Businesses; 7.3. Conclusion; Acknowledgment; References

8. Stochastic analysis on loop groups Shizan Fang

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

981-4383-58-9