Review Articles

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

Liming Zhang ,

Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE, School of Statistics, East China Normal University, Shanghai, Peoples Republic of China

Rongming Wang ,

Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE, School of Statistics, East China Normal University, Shanghai, Peoples Republic of China

Jiaqin Wei

Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE, School of Statistics, East China Normal University, Shanghai, Peoples Republic of China

Pages 214-227 | Received 03 Jun. 2019, Accepted 25 Nov. 2019, Published online: 30 Jan. 2020,
  • Abstract
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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.


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