Asset liability management under sequential stochastic dominance constraints

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 (MSP) 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 asset-liability management problem.