Set optimization - a rather short introduction

Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems

Sequential multi-criterion decision making

In this paper we consider a simple sequential multicriterion decision making problem in which a decision maker has to accept or reject a series of multi-attributed outcomes. We show that using very simple programming techniques, a great deal of the decision making can be automated. The method might be applicable to situations in which a dealer is having to consider sequential offers in a trading market.

Multiobjective investment planning under uncertainty

In this paper we consider the relevance of various planning methods and decision criteria to multiobjective investment planning under uncertainty. Assuming that a natural reaction to uncertainty is to operate so as to leave open as many good options as possible (as opposed to maximizing subjective expected utility) we argue that the planning process should concentrate on analyzing the effects of the initial decision, and that for this exercise the classical methods of mixed integer programming are inappropriate. We demonstrate how the technique of dynamic programming can be extended to take account of multiple objectives and use dynamic programming as a framework in which we analyze the robustness of an initial decision in the face of various types of uncertainty. In so doing we also analyze the risks involved in both the planning and decision making functions.

Polynomial yield curve models for tilting portfolios

In this paper we will discuss the problem of the desired level of accuracy in model specification. In particular we will look at the effect of various polynomial representations of the yield curve on the tilting of medium to long term bond portfolios. As will be seen, the tilting of these portfolios is very sensitive to the degree of the polynomial used for estimating the yield curve, implying that great care must be taken when forecasting any changes in the structure of the yield curve for such an exercise.forecasting goal programming portfolio analysis

A posteriori trade-off analysis in reference point approaches

This paper is concerned with extensions to existing reference point methods for multiple objective decision making (MODM) through the incorporation of an a-posteriori trade-off analysis, i.e. an examination of the tradeoffs between objectives which are implied by a given, tentative solution to the problem under consideration. The term reference point method is used in this context to include both conventional goal programming approaches, where the reference point represents the decision maker’s actual aspiration levels (cf. Lee 1972; Ignizio 1976), and the more recent interactive procedures where the reference point is used as a primarily technical means of exploring the feasible region (Wierzbicki 1979a, 1979b; Lewandowski and Grauer 1982)