Mean‐variance principle of managing cointegrated risky assets and random liabilities

Using the diffusion limit of the discrete‐time error correction model of cointegration for risky assets and geometric Brownian motion for the value of liabilities, we solve the asset‐liability management (ALM) problem using the theory of backward stochastic differential equations. The solutions of the ALM policy and the efficient frontier in terms of surplus are obtained as closed‐form formulas. We numerically examine the impact of cointegration to the trade‐off between risk and return in managing cointegrated risky assets and random liabilities.