Arjan B. Berkelaar

Optimal Portfolio Choice under Loss Aversion

This paper analyzes the optimal investment strategy for loss averse investors, assuming a complete market and general Ito processes for the asset prices. The loss-averse investor follows a partial portfolio insurance strategy. When the investors planning horizon is short (less than 5 years), he or she considerably reduces the initial portfolio weight of stocks compared to an investor with smooth power utility. The empirical section of the paper estimates the level of loss aversion implied by historical U.S. stock market data, using a representative agent model. We find that loss aversion and risk aversion cannot be disentangled empirically.

The Optimal Set and Optimal Partition Approach to Linear and Quadratic Programming

In this chapter we describe the optimal set approach for sensitivity analysis for LP. We show that optimal partitions and optimal sets remain constant between two consecutive transition-points of the optimal value function. The advantage of using this approach instead of the classical approach (using optimal bases) is shown. Moreover, we present an algorithm to compute the partitions, optimal sets and the optimal value function. This is a new algorithm and uses primal and dual optimal solutions. We also extend some of the results to parametric quadratic programming, and discuss differences and resemblances with the linear programming case.

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.

A Primal-Dual Decomposition Algorithm for Multistage Stochastic Convex Programming

This paper presents a new and high performance solution method for multistage stochastic convex programming. Stochastic programming is a quantitative tool developed in the field of optimization to cope with the problem of decision-making under uncertainty. Among others, stochastic programming has found many applications in finance, such as asset-liability and bond-portfolio management. However, many stochastic programming applications still remain computationally intractable because of their overwhelming dimensionality. In this paper we propose a new decomposition algorithm for multistage stochastic programming with a convex objective and stochastic recourse matrices, based on the path-following interior point method combined with the homogeneous self-dual embedding technique. Our preliminary numerical experiments show that this approach is very promising in many ways for solving generic multistage stochastic programming, including its superiority in terms of numerical efficiency, as well as the flexibility in testing and analyzing the model.

Polynomial primal-dual cone affine scaling for semidefinite programming

In this paper we generalize the primal--dual cone affine scaling algorithm of Sturm and Zhang to semidefinite programming.We show in this paper that the underlying ideas of the cone affine scaling algorithm can be naturely applied to semidefiniteprogramming, resulting in a new algorithm. Compared to other primal--dual affine scaling algorithms for semidefiniteprogramming (see, De Klerk, Roos and Terlaky), our algorithm enjoys the lowest computationalcomplexity.

Basis- and partition identification for quadratic programming and linear complementarity problems

Abstract.Optimal solutions of interior point algorithms for linear and quadratic programming and linear complementarity problems provide maximally complementary solutions. Maximally complementary solutions can be characterized by optimal partitions. On the other hand, the solutions provided by simplex–based pivot algorithms are given in terms of complementary bases. A basis identification algorithm is an algorithm which generates a complementary basis, starting from any complementary solution. A partition identification algorithm is an algorithm which generates a maximally complementary solution (and its corresponding partition), starting from any complementary solution. In linear programming such algorithms were respectively proposed by Megiddo in 1991 and Balinski and Tucker in 1969. In this paper we will present identification algorithms for quadratic programming and linear complementarity problems with sufficient matrices. The presented algorithms are based on the principal pivot transform and the orthogonality property of basis tableaus.

Advanced Risk Budgeting Techniques

Publisher Summary Risk budgeting techniques assist funds in making trade-off in a rational way. Risk budgeting is an integrated dynamic risk management process that involves risk measurement, risk attribution, and risk allocation. The process gives valuable insight into the hot spots in the portfolio and the clues for improving the risk-adjusted return. There are various strategies with risk budgeting. The strategic asset allocation determines the return and risk of the fund more than any other investment decision; therefore, the allocation requires considerable care and deliberation. Most large institutional investors have future liabilities such as pension payments or life insurance claims, which need to be paid from the fund. Therefore, the strategic asset allocation decision typically involves a trade-off between maximizing the return of the fund and minimizing the likelihood that the value of the investments of the fund drops below the value of the liabilities. Moreover, pension funds and insurance companies also have to deal with the solvency constraints imposed by regulators. The task of finding an appropriate strategic asset allocation policy for institutional investors with liabilities is known as an asset-liability management problem.