Minimum probability function of crossing the upper regulatory threshold for asset-liability management

In this paper, a stochastic model of asset-liability multiple is considered. To avoid the unbearable investment risk of asset price collapse, an upper regulatory threshold constraint is imposed on the asset-liability multiple. A Hamilton-Jacobi-Bellman (HJB) equation is established using the stochastic optimal control technique. The explicit minimum probability function and the optimal investment strategy are obtained, meanwhile, a verification theorem is also proved. Numerical examples illustrate the effectiveness of our results, which indicates that the current level and the upper regulatory threshold have significant influences on the minimum probability function.