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A numerical approach to optimal dividend policies with capital injections and transaction costs

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Abstract

This work focuses on numerical methods for finding optimal dividend payment and capital injection policies to maximize the present value of the difference between the cumulative dividend payment and the possible capital injections. Using dynamic programming principle, the value function obeys a quasi-variational inequality (QVI). The state constraint of the impulsive control gives rise to a capital injection region with free boundary. Since the closed-form solutions are virtually impossible to obtain, we use Markov chain approximation techniques to construct a discrete-time controlled Markov chain to approximate the value function and optimal controls. Convergence of the approximation algorithms is proved.

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Acknowledgements

We are grateful to the anonymous referee for his/her valuable comments and suggestions.

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Authors and Affiliations

  1. Centre for Actuarial Studies, Department of Economics, the University of Melbourne, Melbourne, VIC, 3010, Australia

    Zhuo Jin

  2. Department of Statistics and Actuarial Science, the University of Hong Kong, Hong Kong, China

    Hai-liang Yang

  3. Department of Mathematics, Wayne State University, Detroit, Michigan, 48202, USA

    G. Yin

Authors
  1. Zhuo Jin
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  2. Hai-liang Yang
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  3. G. Yin
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Corresponding author

Correspondence to Zhuo Jin.

Additional information

This research was supported in part by Early Career Research Grant and Faculty Research Grant by The University of Melbourne. The research of H. Yang was supported in part by Research Grants Council of the Hong Kong Special Administrative Region (project No. HKU 17330816) and Society of Actuaries’ Centers of Actuarial Excellence Research Grant. The research of G. Yin was supported in part by U.S. Army Research Office under grant W911NF-15-1-0218.

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Jin, Z., Yang, Hl. & Yin, G. A numerical approach to optimal dividend policies with capital injections and transaction costs. Acta Math. Appl. Sin. Engl. Ser. 33, 221–238 (2017). https://doi.org/10.1007/s10255-017-0653-6

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  • DOI: https://doi.org/10.1007/s10255-017-0653-6

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