A MARTINGALE APPROACH FOR ASSET ALLOCATION WITH DERIVATIVE SECURITY AND HIDDEN ECONOMIC RISK

Ken Siu; Jinxia Zhu; Hailiang Yang

doi:10.1017/jpr.2019.40

A MARTINGALE APPROACH FOR ASSET ALLOCATION WITH DERIVATIVE SECURITY AND HIDDEN ECONOMIC RISK

Ken Siu^*
, Jinxia Zhu
, Hailiang Yang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

Asset allocation with a derivative security is studied in a hidden, Markovian regimeswitching, 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.

Original language	English
Pages (from-to)	723-749
Journal	Journal of Applied Probability
Volume	56
Issue number	3
DOIs	https://doi.org/10.1017/jpr.2019.40
Publication status	Published - 2019
Externally published	Yes

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abstract = "Asset allocation with a derivative security is studied in a hidden, Markovian regimeswitching, 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.",

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AB - Asset allocation with a derivative security is studied in a hidden, Markovian regimeswitching, 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.

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A MARTINGALE APPROACH FOR ASSET ALLOCATION WITH DERIVATIVE SECURITY AND HIDDEN ECONOMIC RISK

Abstract

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