Research Article
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Year 2018, Volume: 47 Issue: 3, 763 - 781, 01.06.2018

Abstract

References

  • Bai, L. H., Zhang, H. Y.Dynamic mean-variance problem with constrained risk control for the insurers, Mathematical Methods of Operations Research 68 (1), 181-205, 2008.
  • Bäuerle N. Benchmark and mean-variance problems for insurers, Mathematical Methods of Operations Research 62 (1), 159-165, 2005.
  • Bi, J. N, Meng, Q. B., Zhang, Y. J. Dynamic mean-variance and optimal reinsurance problems under the no-bankruptcy constraint for an insurer, Annals of Operations Research 212 (1), 43-59, 2014.
  • Bielecki, T. R., Jang, I. Portfolio optimization with a defaultable security, Asia-Pacic Financial Markets 13 (2), 113-127, 2006.
  • Björk, T., Murgoci, A. A general theory of Markovian time inconsistent stochastic control problems, Working Paper, Stockholm School of Economics, 2009.
  • Björk, T., Murgoci, A., Zhou, X. Y. Mean-variance portfolio optimization with state- dependent risk aversion, Mathematical Finance 24 (1), 1-24, 2014.
  • Browne, S. Optimal investment policies for a rm with random risk process: exponential utility and minimizing the probability of ruin, Mathematics of Operations Research 20, 937-958, 1995.
  • Bo, L., Tang, D., Wang, Y., et al. On the conditional default probability in a regulated market: a structural approach, Quantitative Finance 11 (12), 1695-1702, 2011.
  • Capponi, A., Figueroa-López, J. E. Dynamic portfolio optimization with a defaultable secu- rity and regime-switching, Mathematical Finance 24 (2),207-249, 2014.
  • Chen, P., Yam, S. C. P. Optimal proportional reinsurance and investment with regime- switching for mean-variance insurers, Insurance: Mathematics and Economics 53 (3), 871- 883, 2013.
  • Due, D., Singleton, K. J. Credit risk: pricing, management, and measurement, Princeton University Press, Princeton., 2003.
  • Hipp, C., Plum, M. Optimal investment for insurers, Insurance: Mathematics and Economics 27, 215-228, 2000.
  • Kryger, E. M., Steensen, M. Some solvable portfolio problems with quadratic and collective objectives, Working Paper, University of Copenhagen, 2010.
  • Li, D. P, Rong, X. M., Zhao, H. Time-consistent reinsurance investment strategy for an insurer and a reinsurer with mean-variance criterion under the CEV model, Journal of Computational and Applied Mathematics 283, 142-162, 2015.
  • Korn, R. Kraft, H. Optimal portfolios with defaultable securities a rm value approach, International Journal of Theoretical and Applied Finance 6 (08), 793-819, 2003.
  • Promislow, D. S., Young, V. R. Minimizing the probability of ruin when claims follow Brownian motion with drift, North American Actuarial Journal 9, 109-128, 2005.
  • Shen, Y., Zeng, Y. Optimal investment-reinsurance with delay for mean-variance insurers: A maximum principle approach, Insurance: Mathematics and Economics 57, 1-12, 2014.
  • Shen, Y., Zeng, Y. Optimal investment-reinsurance strategy for mean-variance insurers with square-root factor process, Insurance: Mathematics and Economics 62, 118-137, 2015.
  • Zeng, Y., Li, Z. F., Liu, J. J. Optimal strategies of benchmark and mean-variance portfolio selection problems for insurers, Journal of Industrial and Management Optimization 6 (3), 483-496, 2010.
  • Zeng, Y., Li, Z. F. Optimal time-consistent investment and reinsurance policies for mean- variance insurers, Insurance: Mathematics and Economics 49 (1),145-154, 2011.
  • Zeng, Y., Li, Z. F., Lai, Y. Z. Time-consistent investment and reinsurance strategies for mean-variance insurers with jumps, Insurance: Mathematics and Economics 52 (3), 498- 507, 2013.
  • Zhao, H., Shen, Y., Zeng, Y. Time-consistent investment-reinsurance strategy for mean- variance insurers with a defaultable security, Journal of Mathematical Analysis and Applications 437, 1036-1057, 2016.
  • Zhu, H., Deng, C., Yue, S., et al. Optimal reinsurance and investment problem for an insurer with counterparty risk, Insurance: Mathematics and Economics 61, 242-254, 2015.

Time-consistent reinsurance-investment strategy for mean-variance insurers with defaultable security and jumps

Year 2018, Volume: 47 Issue: 3, 763 - 781, 01.06.2018

Abstract

This paper studies an optimal reinsurance-investment problem for a mean-variance insurer with defaultable security and jumps. Specially, we assume that the risky asset's price process is described by a geometric Lévy process. By using a game theoretic approach, we establish the extended Hamilton-Jacobi-Bellman system for the post-default case and the pre-default case, respectively. Furthermore, we derive the closed-from expressions for the time-consistent reinsurance-investment strategy and the corresponding value function. Finally, we provide numerical examples to illustrate the impacts of model parameters on the time-consistent strategy.

References

  • Bai, L. H., Zhang, H. Y.Dynamic mean-variance problem with constrained risk control for the insurers, Mathematical Methods of Operations Research 68 (1), 181-205, 2008.
  • Bäuerle N. Benchmark and mean-variance problems for insurers, Mathematical Methods of Operations Research 62 (1), 159-165, 2005.
  • Bi, J. N, Meng, Q. B., Zhang, Y. J. Dynamic mean-variance and optimal reinsurance problems under the no-bankruptcy constraint for an insurer, Annals of Operations Research 212 (1), 43-59, 2014.
  • Bielecki, T. R., Jang, I. Portfolio optimization with a defaultable security, Asia-Pacic Financial Markets 13 (2), 113-127, 2006.
  • Björk, T., Murgoci, A. A general theory of Markovian time inconsistent stochastic control problems, Working Paper, Stockholm School of Economics, 2009.
  • Björk, T., Murgoci, A., Zhou, X. Y. Mean-variance portfolio optimization with state- dependent risk aversion, Mathematical Finance 24 (1), 1-24, 2014.
  • Browne, S. Optimal investment policies for a rm with random risk process: exponential utility and minimizing the probability of ruin, Mathematics of Operations Research 20, 937-958, 1995.
  • Bo, L., Tang, D., Wang, Y., et al. On the conditional default probability in a regulated market: a structural approach, Quantitative Finance 11 (12), 1695-1702, 2011.
  • Capponi, A., Figueroa-López, J. E. Dynamic portfolio optimization with a defaultable secu- rity and regime-switching, Mathematical Finance 24 (2),207-249, 2014.
  • Chen, P., Yam, S. C. P. Optimal proportional reinsurance and investment with regime- switching for mean-variance insurers, Insurance: Mathematics and Economics 53 (3), 871- 883, 2013.
  • Due, D., Singleton, K. J. Credit risk: pricing, management, and measurement, Princeton University Press, Princeton., 2003.
  • Hipp, C., Plum, M. Optimal investment for insurers, Insurance: Mathematics and Economics 27, 215-228, 2000.
  • Kryger, E. M., Steensen, M. Some solvable portfolio problems with quadratic and collective objectives, Working Paper, University of Copenhagen, 2010.
  • Li, D. P, Rong, X. M., Zhao, H. Time-consistent reinsurance investment strategy for an insurer and a reinsurer with mean-variance criterion under the CEV model, Journal of Computational and Applied Mathematics 283, 142-162, 2015.
  • Korn, R. Kraft, H. Optimal portfolios with defaultable securities a rm value approach, International Journal of Theoretical and Applied Finance 6 (08), 793-819, 2003.
  • Promislow, D. S., Young, V. R. Minimizing the probability of ruin when claims follow Brownian motion with drift, North American Actuarial Journal 9, 109-128, 2005.
  • Shen, Y., Zeng, Y. Optimal investment-reinsurance with delay for mean-variance insurers: A maximum principle approach, Insurance: Mathematics and Economics 57, 1-12, 2014.
  • Shen, Y., Zeng, Y. Optimal investment-reinsurance strategy for mean-variance insurers with square-root factor process, Insurance: Mathematics and Economics 62, 118-137, 2015.
  • Zeng, Y., Li, Z. F., Liu, J. J. Optimal strategies of benchmark and mean-variance portfolio selection problems for insurers, Journal of Industrial and Management Optimization 6 (3), 483-496, 2010.
  • Zeng, Y., Li, Z. F. Optimal time-consistent investment and reinsurance policies for mean- variance insurers, Insurance: Mathematics and Economics 49 (1),145-154, 2011.
  • Zeng, Y., Li, Z. F., Lai, Y. Z. Time-consistent investment and reinsurance strategies for mean-variance insurers with jumps, Insurance: Mathematics and Economics 52 (3), 498- 507, 2013.
  • Zhao, H., Shen, Y., Zeng, Y. Time-consistent investment-reinsurance strategy for mean- variance insurers with a defaultable security, Journal of Mathematical Analysis and Applications 437, 1036-1057, 2016.
  • Zhu, H., Deng, C., Yue, S., et al. Optimal reinsurance and investment problem for an insurer with counterparty risk, Insurance: Mathematics and Economics 61, 242-254, 2015.
There are 23 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Statistics
Authors

Qiang Zhang This is me

Qianqian Cui This is me

Ping Chen This is me

Publication Date June 1, 2018
Published in Issue Year 2018 Volume: 47 Issue: 3

Cite

APA Zhang, Q., Cui, Q., & Chen, P. (2018). Time-consistent reinsurance-investment strategy for mean-variance insurers with defaultable security and jumps. Hacettepe Journal of Mathematics and Statistics, 47(3), 763-781.
AMA Zhang Q, Cui Q, Chen P. Time-consistent reinsurance-investment strategy for mean-variance insurers with defaultable security and jumps. Hacettepe Journal of Mathematics and Statistics. June 2018;47(3):763-781.
Chicago Zhang, Qiang, Qianqian Cui, and Ping Chen. “Time-Consistent Reinsurance-Investment Strategy for Mean-Variance Insurers With Defaultable Security and Jumps”. Hacettepe Journal of Mathematics and Statistics 47, no. 3 (June 2018): 763-81.
EndNote Zhang Q, Cui Q, Chen P (June 1, 2018) Time-consistent reinsurance-investment strategy for mean-variance insurers with defaultable security and jumps. Hacettepe Journal of Mathematics and Statistics 47 3 763–781.
IEEE Q. Zhang, Q. Cui, and P. Chen, “Time-consistent reinsurance-investment strategy for mean-variance insurers with defaultable security and jumps”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 3, pp. 763–781, 2018.
ISNAD Zhang, Qiang et al. “Time-Consistent Reinsurance-Investment Strategy for Mean-Variance Insurers With Defaultable Security and Jumps”. Hacettepe Journal of Mathematics and Statistics 47/3 (June 2018), 763-781.
JAMA Zhang Q, Cui Q, Chen P. Time-consistent reinsurance-investment strategy for mean-variance insurers with defaultable security and jumps. Hacettepe Journal of Mathematics and Statistics. 2018;47:763–781.
MLA Zhang, Qiang et al. “Time-Consistent Reinsurance-Investment Strategy for Mean-Variance Insurers With Defaultable Security and Jumps”. Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 3, 2018, pp. 763-81.
Vancouver Zhang Q, Cui Q, Chen P. Time-consistent reinsurance-investment strategy for mean-variance insurers with defaultable security and jumps. Hacettepe Journal of Mathematics and Statistics. 2018;47(3):763-81.