Asset liability management under sequential stochastic dominance constraints

Abstract

We consider a financial intermediary managing assets and liabilities exposed to several risk sources and seeking an optimal portfolio strategy to minimise the initial capital invested and the total risk associated with investment losses and financial debt. We formulate the problem as a multistage stochastic programming model, with a time-consistent dynamic risk measure in the objective function to control the investment risk. To ensure that the intermediary's financial equilibrium is preserved, we introduce a funding constraint in the model by enforcing in a time-consistent manner a sequential second-order stochastic dominance (SSD) of the portfolio return distribution over the liability distribution. We demonstrate that imposing the SSD constraint at the last-but-one stage is sufficient to enforce the SSD ordering at each stage. To deal with the computational burden of associated MSP, we develop a novel decomposition scheme integrating, for the first time in the literature, time-consistent dynamic risk measures and sequential stochastic dominance constraints. The proposed methodology is computationally validated on a case study developed on a property and casualty ALM problem.