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...

In this paper we deal with sensitivity analysis in convex quadratic programming, without making assumptions on nondegeneracy, strict convexity of the objective function, and the existence of a strictly complementary solution. We show that the optimal value as a function of a right--hand side...

Asset liability management (ALM) is an important and challenging problem for institutional investors and financial intermediaries. The requirement to fulfill its liablilities constrains the institutional investor in its asset allocation possiblilites. We formulate an ALM model for pension funds...

This paper considers dynamic asset allocation in a mean versus downside-risk framework. We derive closed-form solutions for the optimal portfolio weights when returns are lognormally distributed. Moreover, we study the impact of skewed and fat-tailed return distributions. We find that the...

In 1996 Alan Greenspan warned that stock prices were "unduly escalated" and reflected "irrational exuberance". In this paper we describe an economy that can support a prolonged surge of asset prices, accompanied by a sharp increase of volatility. We study an equilibrium model where some agents...

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 that has found applications in, e.g. finance, such as asset-liability and bond-portfolio management. Computationally...

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 semidefinite programming, resulting in a new algorithm....

Prospect theory and loss aversion play a dominant role in behavioral finance. In this paper we derive closed-form solutions for optimal portfolio choice under loss aversion. When confronted with gains a loss averse investor behaves similar to a portfolio insurer. When confronted with losses, the...

Optimal solutions of interior point algorithms for linear and quadratic programming and linear complementarity problems provide maximal complementary solutions. Maximal complementary solutions can be characterized by optimal (tri)partitions. On the other hand, the solutions provided by...

People are concerned about maintaining purchasing power in times of rising inflation. We formulate investment objectives in terms of real wealth, assuming investors derive utility from the number of goods they can buy with their monetary wealth. We derive closed-form solutions for the portfolio...