The paper's objective is to interpret no-arbitrage conditions by means of linear programming. Basic statements about the term structure of a market with frictions can be derived using the relation of primal and associated dual programs. The duality concept applies mutatis mutandis to the valuation of cash flows from an individual investor's point of view.
Arbitrage theory is based on a single fundamental assumption corresponding to an intuitively straightforward principle: 'There is no free lunch!'. Basically, market participants are all assumed to be greedy, i.e. they prefer more to less. This reasoning results in the existence of equilibrium prices. Depending on the economic context, prices refer to assets, states, interest rates, etc. A basic model of the no arbitrage approach applies to the one-period setting with different outcome states as well as to the multiperiod deterministic context. A generalization can be formulated applicable to the multiperiod stochastic situation including both payments and frictions. It allows pricing within the framework of discrete models obtained by scenario tree analysis, for instance.
Bodensatzprodukte besitzen ein erhebliches, vielfach unzureichend genutztes Ertragspotential. Die konventionelle Wiederanlagemethode, diese Bodensatzprodukte mit konstanter Aufteilung in Festzinsanlagen zu transformieren, schöpft dieses Potenzial nur unzureichend aus. Eine dynamische Bewirtschaftung ist den üblichen statischen Verfahren sowohl unter Risiko- als auch Ertragsgesichtspunkten überlegen.
Das Zinsdifferenzgeschäft stellt für viele Banken eine wesentliche Ertragssäule dar. Dabei ist naturgemäss die Unsicherheit zukünftiger Zinsen und Zahlungsströme die zentrale Herausforderung im Asset-/Liability-Management jeder Bank. Gerade Bodensatzprodukte bieten ein erhebliches Ertragspotenzial. Konventionelle Ansätze, die solch eine variable Position gemäss einer konstanten Aufteilung in ein Portfolio aus Festzinsgeschäften transformieren, werden dem nur unzureichend gerecht. Die Untersuchungen zeigen, dass eine dynamische Bewirtschaftung den üblichen statischen Verfahren sowohl unter Risiko- wie auch Ertragsgesichtspunkten überlegen ist.
The presentation intends to provide insights into the basic ideas of stochastic programming (a field of activity within mathematical programming) paying particular attention to the methodological concept of barycentric approximation. It will be presented in light of an actual problem: the optimal funding of variable rate mortgages.
The complexity of the interaction between time and uncertainty made finance models to one of the most important applications of probability theory and optimization theory. Stochastic programming combines those two fields with the intention to design methodologies for planning under uncertainty. This tutorial consists of two parts, written for practitioners, in particular financial decision makers. It is to provide insights into the basic ideas of stochastic programming in an easily understandable way. This paper reveals various decision structures of investors and evaluates the profits achieved by admissible decisions. Criteria are presented which help identify the optimality of admissible decisions. Further, the optimal profit function is introduced to measure the sensitivity of optimal portfolios with respect to changes in income and term structure. In particular, the saddle property of the optimal profit function is verified with respect to different income and interest rate scenarios. This part concludes with a discussion on the stability of the optimal decisions and the usage of sensitivity results for analyzing the stochastic data with respect to the underlying investor's decision structure.
The stochastic programming methodology applied to the Markowitz approach yields a multistage mean-variance model. The structural properties of the efficient portfolios and the efficient frontiers are derived taking into consideration stochastic dynamic evolvements of the variance-covariance matrices and expected rates of returns over a finite, discrete planning horizon. An aggregation principle is introduced which allows for solving a deterministic convex quadratic single period equivalence program.
