Path-dependent scenario trees for multistage stochastic programmes in finance

The formulation of dynamic stochastic programmes for financial applications generally requires the definition of a risk--reward objective function and a financial stochastic model to represent the uncertainty underlying the decision problem. The solution of the optimization problem and the quality of the resulting strategy will depend critically on the adopted financial model and its consistency with observed market dynamics. We present a recursive scenario approximation approach suitable for financial management problems, leading to a minimal yet sufficient representation of the randomness underlying the decision problem. The method relies on the definition of a benchmark probability space generated through Monte Carlo simulation and the implementation of a scenario reduction scheme. The procedure is tested on an interest rate vector process capturing market and credit risk dynamics in the fixed income market. The collected results show that a limited number of scenarios is sufficient to capture the exposure of the decision maker to interest rate and default risk.