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Dynamic asset allocation with loss aversion in a jump-diffusion model

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Abstract

This paper investigates a dynamic asset allocation problem for loss-averse investors in a jump-diffusion model where there are a riskless asset and N risky assets. Specifically, the prices of risky assets are governed by jump-diffusion processes driven by an m-dimensional Brownian motion and a (N − m)-dimensional Poisson process. After converting the dynamic optimal portfolio problem to a static optimization problem in the terminal wealth, the optimal terminal wealth is first solved. Then the optimal wealth process and investment strategy are derived by using the martingale representation approach. The closed-form solutions for them are finally given in a special example.

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Authors and Affiliations

  1. School of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University, Nanjing, 210023, China

    Hui Mi

  2. Department of Statistics and Finance, University of Science and Technology of China, Hefei, 230026, China

    Hui Mi, Xiu-chun Bi & Shu-guang Zhang

Authors
  1. Hui Mi
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  2. Xiu-chun Bi
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  3. Shu-guang Zhang
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Corresponding author

Correspondence to Hui Mi.

Additional information

Supported by the National Natural Science Foundation of China (No.61304065, 11471304, 11401556), and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No.12KJB110011).

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Mi, H., Bi, Xc. & Zhang, Sg. Dynamic asset allocation with loss aversion in a jump-diffusion model. Acta Math. Appl. Sin. Engl. Ser. 31, 557–566 (2015). https://doi.org/10.1007/s10255-015-0485-1

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  • DOI: https://doi.org/10.1007/s10255-015-0485-1

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