Mean–variance asset–liability management: Cointegrated assets and insurance liability - Chiu, Mei Choi; Wong, Hoi Ying (European journal of operational research, 2012)
► Consider the mean–variance ALM for an insurer investing in cointegrated assets. ► The insurer has random insurance claims during the investment period. ► The problem is solved by generalizing the approach in Lim (2005). ► The optimal control is obtained in explicit and closed-form formulas. ► Numerical examples show that cointegration is important to ALM. The cointegration of major financial markets around the globe is well evidenced with strong empirical support. This paper considers the continuous-time mean–variance (MV) asset–liability management (ALM) problem for an insurer investing in an incomplete financial market with cointegrated assets. The number of trading assets is allowed to be less than the number of Brownian motions spanning the market. The insurer also faces the risk of paying uncertain insurance claims during the investment period. We assume that the cointegration market follows the diffusion limit of the error-correction model for cointegrated time series. Using the Markowitz (1952) MV portfolio criterion, we consider the insurer’s problem of minimizing variance in the terminal wealth, given an expected terminal wealth subject to interim random liability payments following a compound Poisson process. We generalize the technique developed by Lim (2005) to tackle this problem. The particular structure of cointegration enables us to solve the ALM problem completely in the sense that the solutions of the continuous-time portfolio policy and efficient frontier are obtained as explicit and closed-form formulas.