Nalan Gulpinar

Simulation and optimization approaches to scenario tree generation

In this paper, three approaches are presented for generating scenario trees for 3nancial portfolio problems. These are based on simulation, optimization and hybrid simulation/optimization. In the simulation approach, the price scenarios at each time period are generated as the centroids of random scenario simulations generated sequentially or in parallel. The optimization method generates a number of discrete outcomes which satisfy speci3ed statistical properties by solving either a sequence of non-linear optimization models (one at each node of the scenario tree) or onelargeoptimization proble m. In thehybrid approach, theoptimization proble m is re duce d in size by 3xing price variables to values obtained by simulation. These procedures are backtested using historical data and computational results are presented. ? 2003 Elsevier B.V. All rights reserved.

Worst-case robust decisions for multi-period mean-variance portfolio optimization

Abstract In this paper, we extend the multi-period mean–variance optimization framework to worst-case design with multiple rival return and risk scenarios. Our approach involves a min–max algorithm and a multi-period mean–variance optimization framework for the stochastic aspects of the scenario tree. Multi-period portfolio optimization entails the construction of a scenario tree representing a discretised estimate of uncertainties and associated probabilities in future stages. The expected value of the portfolio return is maximized simultaneously with the minimization of its variance. There are two sources of further uncertainty that might require a strengthening of the robustness of the decision. The first is that some rival uncertainty scenarios may be too critical to consider in terms of probabilities. The second is that the return variance estimate is usually inaccurate and there are different rival estimates, or scenarios. In either case, the best decision has the additional property that, in terms of risk and return, performance is guaranteed in view of all the rival scenarios. The ex-ante performance of min–max models is tested using historical data and backtesting results are presented.

Robust strategies for facility location under uncertainty

This paper considers a stochastic facility location problem in which multiple capacitated facilities serve customers with a single product, and a stockout probabilistic requirement is stated as a chance constraint. Customer demand is assumed to be uncertain and to follow either a normal or an ambiguous distribution. We study robust approximations to the problem in order to incorporate information about the random demand distribution in the best possible, computationally tractable way. We also discuss how a decision maker’s risk preferences can be incorporated in the problem through robust optimization. Finally, we present numerical experiments that illustrate the performance of the different robust formulations. Robust optimization strategies for facility location appear to have better worst-case performance than nonrobust strategies. They also outperform nonrobust strategies in terms of realized average total cost when the actual demand distributions have higher expected values than the expected values used as input to the optimization models.

Extracting pure network submatrices in linear programs using signed graphs

It is shown that the problem of detecting a maximum embedded network in a linear program is related to balancing of subgraphs of signed graphs. This approach leads to a simple efficient heuristic to extract an embedded network. The proposed heuristic also determines whether a given linear program is a (reflected) network itself. Some complexity results are obtained and computational results are also reported.

Robust investment strategies with discrete asset choice constraints using DC programming

In this article, we are concerned with robust investment strategies for the portfolio management problem. We extend the classical Markowitz framework with discrete asset choice constraints to worst-case portfolio selection with rival risk and return scenario specifications. Robustness is ensured by considering the optimal strategy in view of multiple rival scenarios and evaluating the portfolio simultaneously with the worst-case scenario. Discrete constraints, such as buy-in thresholds and cardinality, represent the investors choice on the assets. Portfolio allocation with discrete asset choice constraints is a non-convex and NP-hard problem. A local deterministic optimization approach based on difference of convex (DC) functions programming is introduced and a DC algorithm (DCA) is developed to solve min–max mean–variance portfolio optimization problem. The computational results using historical data show that the DCA is more efficient than the standard methods and often provides a global solution.

Multistage Stochastic Programming in Computational Finance

Multistage stochastic programming is used to model the problem of financial portfolio management, given stochastic data provided in the form of a scenario tree. The mean or variance of total wealth at the end of the planning horizon can be optimised by solving either a linear stochastic program or a quadratic stochastic program, respectively; solution of many almost identical quadratic stochastic programs yields points describing the Markowitz efficient frontier. Computational results and backtesting are presented on a number of models, simulated and real.

Robust optimal decisions with imprecise forecasts

A robust minimax approach for optimal investment decisions with imprecise return forecasts and risk estimations in financial portfolio management is considered. Single-period and multi-period mean-variance optimization models are extended to worst-case design with multiple rival risk estimations and return forecasts. In multi-period stochastic formulation of classical mean-variance portfolio optimization problem, an investor makes an investment decision based on expectations and/or scenarios up to some intermediate times prior to the horizon and, consequently, rebalances or restructures the portfolio. Multi-period portfolio optimization entails the construction of a scenario tree representing a discretized estimate of uncertainties and associated probabilities in future stages. It is well known that return forecasts and risk estimations are inherently inaccurate and there are different rival estimates, or scenario trees. Robust optimization models are presented and imprecise nature of moment forecasts to reduce the risk of making a decision based on the wrong scenario is addressed. The worst-case performance is guaranteed in view of all rival risk and return scenarios and will only improve when any scenario other than the worst-case is realized. The ex-ante performance of minimax models is tested using historical data and backtesting results are presented.

Post-tax optimization with stochastic programming

Abstract In this paper, we consider a stochastic programming approach to multistage post-tax portfolio optimization. Asset performance information is specified as a scenario tree generated by two alternative methods based on simulation and optimization. We assume three tax wrappers involving the same instruments for an efficient investment strategy and determine optimal allocations to different instruments and wrappers. The tax rules are integrated with the linear and mixed integer stochastic models to yield an overall tax and return-efficient multistage portfolio. The computational performance of these models is tested using a case study with different scenario trees. Our experiments show that optimal portfolios obtained by both linear programming and mixed integer stochastic models diversify over wrappers and the original capital is distributed among assets within each wrapper.

Analysis of relationship between forward and spot markets in oligopolies under demand and cost uncertainties

In this paper, we consider interaction between spot and forward trading under demand and cost uncertainties, deriving the equilibrium of the multi-player dynamic games. The stochastic programming and worst-case analysis models based on discrete scenarios are developed to analyze the impact of demand uncertainty and risk aversion on oligopoly (forward and spot) markets’ structure in terms of the forwards and spot pricing, traded quantities and production. A real case of the Iberian electricity market is studied to illustrate performance of the models. The numerical experiments show that cost uncertainty impacts on the strategic decisions more than demand uncertainty.

A mixed integer programming model for multistage mean-variance post-tax optimization

Abstract In this paper, we introduce a mixed integer stochastic programming approach to mean–variance post-tax portfolio management. This approach takes into account of risk in a multistage setting and allows general withdrawals from original capital. The uncertainty on asset returns is specified as a scenario tree. The risk across scenarios is addressed using the probabilistic approach of classical stochastic programming. The tax rules are used with stochastic linear and mixed integer quadratic programming models to compute an overall tax and return-risk efficient multistage portfolio. The incorporation of the risk term in the model provides robustness and leads to diversification over wrappers and assets within each wrapper. General withdrawals and risk aversion have an impact on the distribution of assets among wrappers. Computational results are presented using a study with different scenario trees in order to show the performance of these models.