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

Tak Kuen Siu, Jinxia Zhu, Hailiang Yang

Research output: Contribution to journalArticleResearchpeer-review

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.

LanguageEnglish
Pages723-749
Number of pages27
JournalJournal of Applied Probability
Volume56
Issue number3
DOIs
Publication statusPublished - 1 Sep 2019

Fingerprint

Asset Allocation
Martingale
Economics
Derivative
Logarithmic
Exponential Utility
Markovian Switching
Regime Switching
Malliavin Calculus
Utility Function
Elasticity
Filtering
Martingale approach
Derivative securities
Asset allocation
Economic risk
Malliavin calculus
Power utility
Utility function
Exponential utility

Keywords

  • Asset allocation
  • Derivatives
  • Filtering
  • Malliavin calculus

Cite this

@article{2867be137ac94fbcaf9793a461c1c66b,
title = "A martingale approach for asset allocation with derivative security and hidden economic risk",
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 allocation, Derivatives, Filtering, Malliavin calculus",
author = "Siu, {Tak Kuen} and Jinxia Zhu and Hailiang Yang",
year = "2019",
month = "9",
day = "1",
doi = "10.1017/jpr.2019.40",
language = "English",
volume = "56",
pages = "723--749",
journal = "Journal of Applied Probability",
issn = "0021-9002",
publisher = "University of Sheffield",
number = "3",

}

A martingale approach for asset allocation with derivative security and hidden economic risk. / Siu, Tak Kuen; Zhu, Jinxia; Yang, Hailiang.

In: Journal of Applied Probability, Vol. 56, No. 3, 01.09.2019, p. 723-749.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - A martingale approach for asset allocation with derivative security and hidden economic risk

AU - Siu, Tak Kuen

AU - Zhu, Jinxia

AU - Yang, Hailiang

PY - 2019/9/1

Y1 - 2019/9/1

N2 - 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.

AB - 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.

KW - Asset allocation

KW - Derivatives

KW - Filtering

KW - Malliavin calculus

UR - http://www.scopus.com/inward/record.url?scp=85072829099&partnerID=8YFLogxK

UR - http://purl.org/au-research/grants/arc/DP130103517

UR - http://purl.org/au-research/grants/arc/DP1096243

U2 - 10.1017/jpr.2019.40

DO - 10.1017/jpr.2019.40

M3 - Article

VL - 56

SP - 723

EP - 749

JO - Journal of Applied Probability

T2 - Journal of Applied Probability

JF - Journal of Applied Probability

SN - 0021-9002

IS - 3

ER -