Cees L. Dert

A Primal-Dual Decomposition-Based Interior Point Approach to Two-Stage Stochastic Linear Programming

Decision making under uncertainty is a challenge faced by many decision makers. Stochastic programming is a major tool developed to deal with optimization with uncertainties which has found applications in, e.g., finance, such as asset--liability and bond--portfolio management. Computationally, however, many models in stochastic programming remain unsolvable because of overwhelming dimensionality. For a model to be well solvable, its special structure must be explored. Most of the solution methods are based on decomposing the data. In this paper we propose a new decomposition approach for two-stage stochastic programming, based on a direct application of the path-following method combined with the homogeneous self-dual technique. Numerical experiments show that our decomposition algorithm is very efficient for solving stochastic programs. In particular, we apply our decomposition method to a two-period portfolio selection problem using options on a stock index. In this model the investor can invest in a money-market account, a stock index, and European options on this index with different maturities. We experiment with our model with market prices of options on the S&P500.

Optimal Guaranteed Return Portfolios and the Casino Effect

In this paper we address the problem of determining optimal portfolios that may include options in a framework of return maximization with risk constraints relative to a benchmark, as well as in terms of absolute returns. The model we propose allows for deterministic constraints as well as probabilistic constraints. We derive properties of optimal and feasible portfolios and present a linear programming model to solve the problem. The optimal portfolios have payoff functions that reflect a gambling policy. We show that optimal solutions to a large class of portfolio models that maximize expected return subject to downside risk constraints are driven by this casino effect and present tractable conditions under which it occurs in our model. We propose to control the casino effect by using chance constraints. Using results from financial theory, we formulate an LP model that maximizes expected return subject to worst-case return constraints and chance constraints on achieving prespecified levels of return. The results are illustrated with real-life data on the S&P 500 index.

The design and production of new retirement savings products: a note

An earlier contribution to this journal implied that protective floor investment strategies in defined-contribution pension investments beat investments in traditional asset mixes, with respect to both the probability of achieving a minimum target level of future pension income and the expected level of future pension income. These commentators show that protective floor strategies may be attractive to loss-averse investors, but they do not beat traditional investments simultaneously on expected pension income and on the probability of achieving the target pension income.