Asset and Liability Management (ALM) models have been recently recast as Liability-Driven Investment (LDI) models for making integrated financial decisions in pension schemes investment: matching and outperforming a pension plans liabilities. LDI has become extremely popular as the decision tool of choice for pension funds. Market developments and recent accounting and regulatory changes require a pension fund to adopt a new view on their asset allocation decision. We present a generic ALM problem cast as an LDI, which we represent through a family of four decision models: a deterministic linear programming model, a two-stage stochastic programming (SP) model incorporating uncertainty, a chance-constrained SP model and an integrated chance-constrained SP model. In the deterministic model, we study the relationship between PV01 matching and the required funding. In the model, we have two sources of randomness: liabilities and interest rates. We generate interest rate scenarios using the Cox, Ingersoll and Ross model and investigate the relationship between funding requirements and minimize the absolute deviation of the present value matching of the assets and liabilities over time. In the chance-constrained programming model, we limit the number of future deficit events by introducing binary variables and a user-specified reliability level. The fourth model has integrated chance constraints, which not only limits the events of underfunding, but also the amount of underfunding relative to the liabilities. All models employ a buy-and-hold strategy in a fixed-income portfolio, whereas recourse actions are only taken in borrowing and lending.
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