2019/06/20 by Shihao Zhu, Zhu, Shihao, Jingtao Shi +1
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #49L25 #60H10 #93C41 #93E11 #93E20 #FOS: Economics and business #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Mathematical Finance (q-fin.MF) #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1906.08410
openalex publication_date 2019/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is concerned with an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance. The driving Brownian motion and the rate in return of the risky asset price dynamic equation cannot be directly observed. And the short-selling of stocks is prohibited. The problem is formulated as a stochastic linear-quadratic (LQ) optimal control problem where the control variables are constrained. Based on the separation principle and stochastic filtering theory, the partial information problem is solved. Efficient strategies and efficient frontier are presented in closed forms via solutions to two extended stochastic Riccati equations. As a comparison, the efficient strategies and efficient frontier are given by the viscosity solution for the Hamilton-Jacobi-Bellman (HJB) equation in the full information case. Some numerical illustrations are also provided.