Optimal mean-variance reinsurance and investment strategy with constraints in a non-Markovian regime-switching model

Abstract

This paper is devoted to study the proportional reinsurance/new business and investment problem under the mean-variance criterion in a continuous-time setting. The strategies are constrained in the non-negative cone and all coefficients in the model except the interest rate are stochastic processes adapted the filtration generated by a Markov chain. With the help of a backward stochastic differential equation driven by the Markov chain, we obtain the optimal strategy and optimal cost explicitly under this non-Markovian regime-switching model. The cases with one risky asset and Markov regime-switching model are considered as special cases.

Keywords:

• Markov chain
• mean-variance problem
• non-negative constraints
• BSDE
• regime-switching

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 For example, Credit Default Swap (CDS) is a popular credit derivative to enhance the credit ratings of the reference risky assets. Thus, the claim processes of insurers providing CDS protections are related to the financial risks.

Additional information

Funding

This work was supported by the 111 Project [grant number B14019] and the National Natural Science Foundation of China [grant numbers 11571113, 11601157, 11601320].

Notes on contributors

Liming Zhang

Liming Zhang is a Ph.D. candidate, School of Statistics, East China Normal University.

Rongming Wang

Dr Rongming Wang holds a Ph.D. from East China Normal University. He is now a professor at East China Normal University. His research interests include financial risk management, insurance actuarial and mathematical finance.

Jiaqin Wei

Dr Jiaqin Wei holds a Ph.D. from East China Normal University. He is now a research professor at East China Normal University. His research interests include actuarial science and mathematical finance.