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A martingale approach for asset allocation with derivative security and hidden economic risk

Part of: Stochastic analysis Mathematical finance

Published online by Cambridge University Press:  01 October 2019

Tak Kuen Siu ,
Jinxia Zhu  and
Hailiang Yang
Tak Kuen Siu*
Affiliation:
Macquarie University
Jinxia Zhu*
Affiliation:
The University of New South Wales
Hailiang Yang*
Affiliation:
The University of Hong Kong
*
*Postal address: Department of Actuarial Studies and Business Analytics, Macquarie Business School, Macquarie University, Sydney, NSW 2109, Australia.
***Postal address: School of Risk and Actuarial Studies, Business School, The University of New South Wales, Sydney, Australia.
****Postal address: Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong, China.
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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.

Keywords

Asset allocationDerivativesFilteringMalliavin calculus

MSC classification

Primary: 91G10: Portfolio theory
Secondary: 91G20: Derivative securities 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems) 60H07: Stochastic calculus of variations and the Malliavin calculus
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 3 , September 2019 , pp. 723 - 749
Copyright
© Applied Probability Trust 2019 

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