Multi-Period Asset-liability Management with Cash Flows and Probability Constraints: A Mean-Field Formulation Approach

Using a multi-period mean-variance model, we investigate an asset-liability portfolio management problem with probability constraints, where an investor intends to control the probability of bankruptcy before the terminal time in the investment. In our model, the wealth process is influenced not only by return on assets and liability but also by uncontrolled cash flows. Applying a mean-field formulation, we obtain closed-form expressions for an efficient investment strategy and its corresponding mean-variance efficient frontier. Sensitivity analysis is also presented to help investors understand the influences of cash flows and probability constraints better.