A martingale approach for asset allocation with derivative security and hidden economic risk. (September 2019)

• Record Type: Journal Article
• Authors: Siu, Tak Kuen; Zhu, Jinxia; Yang, Hailiang
• Is Part Of: Journal of applied probability. Volume 56:Number 3(2019)
• Page Start: 723
• Page End: 749
• Publication Date: 2019-09
• Subjects: Asset allocation, -- Derivatives, -- Filtering, -- Malliavin calculus; Primary 91G10, -- Secondary 91G20, -- 91G80, -- 60H07; 519.2
• DOI: 10.1017/jpr.2019.40
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract: Asset allocation with a derivative security is studied in a hidden, Markovian regime-switching, economy using filtering theory and the martingale approach. A generalized delta-hedged ratio and a generalized elasticity of an option are introduced to accommodate the presence of the information state process and the derivative security. Malliavin calculus is applied to derive a solution for a general utility function which includes an exponential utility, a power utility, and a logarithmic utility. A compact solution is obtained for a logarithmic utility. Some economic implications of the solutions are discussed.