Viscosity Solution of Mean-Variance Portfolio Selection of a Jump Markov Process with No-Shorting Constraints
Author
Source
Journal of Applied Mathematics
Issue
Vol. 2016, Issue 2016 (31 Dec. 2016), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2016-05-04
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
We consider the so-called mean-variance portfolio selection problem in continuous time under the constraint that the short-selling of stocks is prohibited where all the market coefficients are random processes.
In this situation the Hamilton-Jacobi-Bellman (HJB) equation of the value function of the auxiliary problem becomes a coupled system of backward stochastic partial differential equation.
In fact, the value function V often does not have the smoothness properties needed to interpret it as a solution to the dynamic programming partial differential equation in the usual (classical) sense; however, in such cases V can be interpreted as a viscosity solution.
Here we show the unicity of the viscosity solution and we see that the optimal and the value functions are piecewise linear functions based on some Riccati differential equations.
In particular we solve the open problem posed by Li and Zhou and Zhou and Yin.
American Psychological Association (APA)
Kounta, Moussa. 2016. Viscosity Solution of Mean-Variance Portfolio Selection of a Jump Markov Process with No-Shorting Constraints. Journal of Applied Mathematics،Vol. 2016, no. 2016, pp.1-14.
https://search.emarefa.net/detail/BIM-1107201
Modern Language Association (MLA)
Kounta, Moussa. Viscosity Solution of Mean-Variance Portfolio Selection of a Jump Markov Process with No-Shorting Constraints. Journal of Applied Mathematics No. 2016 (2016), pp.1-14.
https://search.emarefa.net/detail/BIM-1107201
American Medical Association (AMA)
Kounta, Moussa. Viscosity Solution of Mean-Variance Portfolio Selection of a Jump Markov Process with No-Shorting Constraints. Journal of Applied Mathematics. 2016. Vol. 2016, no. 2016, pp.1-14.
https://search.emarefa.net/detail/BIM-1107201
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1107201