Title: Time-consistent mean-variance reinsurance-investment problems under unbounded random parameters: BSDE and Uniqueness
Authors: Hoi Ying Wong - The Chinese University of Hong Kong (Hong Kong) [presenting]
Bingyan Han - The Chinese University of Hong Kong (Hong Kong)
Abstract: The open-loop time-consistent mean-variance (TCMV) reinsurance-investment problem is investigated when the parameters of the stochastic differential equations are stochastic and unbounded. The risk premium process of risky assets can be random and unbounded. Under an exponential integrability condition on the risk premium, we characterize the TCMV reinsurance-investment problem via a BSDE framework. An explicit solution to the equilibrium strategies is derived for a constant risk aversion under several popular financial models, including the constant elasticity of variance (CEV) and Ornstein-Uhlenbeck processes. For state-dependent risk aversion, a semi-closed form solution (up to the solutions to a pair of nonlinear PDEs) is obtained. Numerical results show that, under the CEV model, when stock price goes up, the equilibrium strategies suggest to invest more on the stock and less on the reinsurance protection. Under certain conditions, we prove the uniqueness of equilibrium strategies for constant and state-dependent risk aversion and this supplements results in the literature of using the HJB approach for the feedback controls.