Analytic Decision Rules for Financial Stochastic Programs

Contemporary financial stochastic programs typically involve a trade-offbetween return and (downside)-risk. Using stochastic programming we characterize analytically (rather than numerically) the optimal decisions that follow from characteristic single-stage and multi-stage versions of such programs. The solutions are presented in the form of decision rules with a clear-cut economic interpretation. This facilitates transparency and ease of communication with decision makers. The optimal decision rules exhibit switching behavior in terms of relevant state variables like the assets to liabilities ratio. We find that the model can be tuned easily using Value-at-Risk (VaR) related benchmarks. In the multi-stage setting, we formally prove that the optimal solution consists of a sequence of myopic (single-stage) decisions with risk-aversion increasing over time. The optimal decision rules in the dynamic setting therefore exhibit identical features as in the static context.