Scenario Optimization Asset and Liability Modelling for Individual Investors

We develop a scenario optimization model for asset and liability management ofindividual investors. The individual has a given level of initial wealth and a target goal to bereached within some time horizon. The individual must determine an asset allocation strategyso that the portfolio growth rate will be sufficient to reach the target. A scenario optimizationmodel is formulated which maximizes the upside potential of the portfolio, with limits onthe downside risk. Both upside and downside are measured vis- `a-vis the goal. The stochasticbehavior of asset returns is captured through bootstrap simulation, and the simulation isembedded in the model to determine the optimal portfolio. Post-optimality analysis usingout-of-sample scenarios measures the probability of success of a given portfolio. It alsoallows us to estimate the required increase in the initial endowment so that the probability ofsuccess is improved.