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Mean-Variance Portfolio Selection with a Stochastic Cash Flow in a Markov-switching Jump–Diffusion Market

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Abstract

This paper considers a non-self-financing mean-variance portfolio selection problem in which the stock price and the stochastic cash flow follow a Markov-modulated Lévy process and a Markov-modulated Brownian motion with drift, respectively. The stochastic cash flow can be explained as the stochastic income or liability of the investors during the investment process. The existence of optimal solutions is analyzed, and the optimal strategy and the efficient frontier are derived in closed-form by the Lagrange multiplier technique and the LQ (Linear Quadratic) technique.

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Acknowledgements

This research is supported by grants of Humanity and Social Science Foundation of Ministry of Education of China (No. 12YJCZH219), National Natural Science Foundation of China (No. 71271223).

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Authors and Affiliations

  1. China Institute for Actuarial Science, Central University of Finance and Economics, Beijing, 100081, P.R. China

    Huiling Wu

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  1. Huiling Wu
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Correspondence to Huiling Wu.

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Communicated by Xiaoqi Yang.

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Wu, H. Mean-Variance Portfolio Selection with a Stochastic Cash Flow in a Markov-switching Jump–Diffusion Market. J Optim Theory Appl 158, 918–934 (2013). https://doi.org/10.1007/s10957-013-0292-x

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