Scenario Optimisation

Bernd Scherer

Scenario optimisation is used where the parameters of a mathematical model (asset returns over the next year, for example) are subject to randomness. One way to solve these stochastic programmes is to solve a deterministic problem with many different scenarios assumed for the uncertain inputs – in our case, returns. We can, for example, sample 100,000 scenarios for five assets from the predictive distribution (see Chapter 9) to arrive at a 100,000× 5 cell matrix. After the draws have been made, uncertainty is removed and we are left with the deterministic problem of which asset weights to choose in order to maximise the objective, taking into account what can happen in all 100,000 scenarios. We will see later that for many objectives this can be written as a linear program.11See Dembo (1991), the classic reference for scenario optimisation.

Scenario optimisation investigates how well feasible solutions perform in different scenarios (using an objective function to evaluate the solution for each scenario) and then tries to find the optimal solution. Although future asset returns are uncertain, scenario optimisation attempts to draw representative scenarios that could happen in the

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