Managing risk using multi-stage stochastic optimization, Report SOL

The paper discusses the application of multi-stage stochastic optimization for managing and optimizing expected returns versus risk, and contrasts static (single-stage) versus dynamic (multi-stage) portfolio optimization. We present how to best fund a pool of similar fixed rate mortgages through issuing bonds, callable and non-callable, of various maturities using stochastic optimization. We discuss the estimation of expected net present value and risk for different funding instruments using Monte Carlo sampling techniques, and the optimization of the funding using single- and multi-stage stochastic optimization. Using practical data we computed efficient frontiers of expected net present value versus risk for the single- and the multi-stage model, and studied the underlying funding strategies. Constraining the duration and convexityof the mortgage pool and the funding portfolios to match at anydecision point, we computed delta and gamma hedged funding strategies and compared them to the ones from the multi-stage stochastic optimization model. The results for the different data assumptions demonstrate tha