Working Paper #61, January 2000 (Ini 6)

Sögner

Okun's Law: Does the Austrian Unemployment -- GDP relationship exhibit Structural Breaks?

Okun's Law postulates an inverse relationship between movements of the unemployment rate and the real gross domestic product (GDP). Empirical estimates for US data indicate that a two to three percent GDP growth rate above the natural or average GDP growth rate causes unemployment to decrease by one percentage point and vice versa. In this investigation we check whether this postulated relationship exhibits structural breaks by means of Markov-Chain Monte Carlo methods. We estimate a regression model, where the parameters are allowed to switch between different states and the switching process is Markov. As a by-product we derive an estimate of the current state within the periods considered. Using quarterly Austrian data on unemployment and real GDP from 1977 to 1995 we infer only one state, i.e. there are no structural breaks. The estimated parameters demand for an excess GDP growth rate of 4.16% to decrease unemployment by 1 percentage point. Since only one state is inferred, we conclude that the Austrian economy exhibits a stable relationship between unemployment and GDP growth. 

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Working Paper #62, January 2000 (Ini 3)

Buchta, Dolnicar, Köck, Skriner

A Note on Topological Concepts for Complexity Reduction of Binary Survey Data

Recently in Steiner 1999 the use of topological concepts was suggested for deciding on the level of complexity reduction of continuous data sets by quantisations. Level of complexity is synonymous with the number of classes or class representing means (centroids) of a data partition. In this paper a simulation study of the applicability of this concept to binary data is presented which is comparable with the results in Weingessel et al. 1999. The class of quantisation methods used contains traditional k-means and three robust approaches to partitioning, as suggested in Pötzelberger and Strasser 1997.  

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Working Paper #63, January 2000 (Ini 6)
Revised version

Gaunersdorfer, Hommes

A Nonlinear Structural Model for Volatility Clustering

A simple nonlinear structural model of endogenous belief heterogeneity is proposed. News about fundamentals is an IID random process, but nevertheless volatility clustering occurs as an endogenous phenomenon caused by the interaction between different types of traders, fundamentalists and technical analysts. The belief types are driven by an adaptive, evolutionary dynamics according to the success of the prediction strategies in the recent past conditioned upon price deviations from the rational expectations fundamental price. Asset prices switch irregularly between two different regimes -- close to the fundamental price fluctuations with low volatility, and periods of persistent deviations from fundamentals triggered by technical trading -- thus, creating time varying volatility similar to that observed in real financial data.

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Working Paper #64, January 2000 (Ini 2)

J. Cvitani, H. Wang and W. Schachermayer

Large Utility Maximization in Incomplete Markets with Random Endowment.

This paper solves a long-standing open problem in mathematical finance: to find a solution to the problem of maximizing utility from terminal wealth of an agent with a random endowment process, in the  general, semimartingale model for  incomplete markets, and to characterize it via the associated dual problem. We show that this is indeed possible if the dual problem and its domain are carefully defined. More precisely, we show that the optimal terminal wealth is equal to the inverse of marginal utility evaluated at the solution to the dual problem, which is in the form  of the regular part of an element of $(L^\infty^*)$ (the dual space of $L^\infty$).

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Working Paper #65, January 2000 (Ini 2)

Schachermayer

Optimal Investment in Incomplete Markets when Wealth may Become Negative

TThis paper accompanies a previous one from 1999 by D. Kramkov and the present author [. There, we considered utility functions $U:\R_+ \to \R$ satisfying the Inada conditions $U'(0)=\infty$ and $U'(\infty)=0$, in the present paper we consider utility functions $U:\R\to\R$ which are finitely valued, for all $x\inftyn\R$, and satisfy $U'(-\infty)=\infty$ and $U'(\infty)=0$. A typical example of this situation is the exponential utility $U(x)=- \e^{-x}$.

In the setting of the former paper the following crucial condition on the asymptotic elasticity of $U$, as $x$ tends to $+\infty$, was isolated: $\limsup_{x\to +\infty} \frac{x U'(x)}{U(x)}<1$. This condition was found to be necessary and sufficient for the existence of the optimal investment as well as other key assertions of the related duality theory to hold true, if we allow for general semi-martingales to model a (not necessarily complete) financial market.

In the setting of the present paper this condition has to be accompanied by a similar condition on the asymptotic elasticity of $U$, as $x$ tends to $-\infty$, namely, $\liminf_{x\to-\infty} \frac{x U'(x)}{U(x)}>1$. If both conditions are satisfied --- we then say that the utility function $U$ has reasonable asymptotic elasticity --- we prove an existence theorem for the optimal investment in a general semi-martingale model of a financial market and for a utility function $U:\R\to\R$ , which is finitely valued on all of $\R$; this theorem is parallel to the main result of the former paper. We give examples showing that the reasonable asymptotic elasticity of $U$ also is a necessary condition for several key assertions of the theory to hold true.

D. Kramkov and W. Schachermayer: A Condition on the Asymptotic Elasticity of Utility Functions and Optimal Investment in Incomplete Markets. Annals of Applied Probability, Vol. 9, No. 3, (1999), p. 904 - 950. SFB-Report #25.

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Working Paper #66, ??? (Ini 2)

Hodges, Tompkins

The Sampling Properties of Volatility Cones

In this research, we extend the original work on volatility cones by Burghardt and Lane (1990) to consider of the sampling properties of the variance of variance (and the standard deviation of volatility) under a rich class of models that includes stochastic volatility and conditionally fat-tailed distributions.
Because the volatility cone examines volatility at quite long horizons, the estimation requires the use of overlapping data. This theory confirms the casual observation that the estimation of the variance of variance is downward biased when estimation is done on an overlapping basis. Our principal contribution is to identify what this bias is and derive an adjustment factor that approximates an unbiased estimate of the true variance of variance when overlapping data is used. Another contribution is the derivation of a formula that describes the variance of the quadratic variation over different time horizons.
Using the theory presented, we tested the bias adjustments to the standard deviation of volatility using simulations. Two cases were examined: a GBM i.i.d. process and a non-i.i.d. process associated with the stochastic volatility model suggested by Heston (1993). For both cases, the theoretical adjustments remove almost all the bias introduced by estimation of volatility with overlapping data.
These results are relevant to those who must sell options and must understand the nature of quadratic variation in asset prices. This will provide clearer insights into the nature of hedging errors when dynamically hedging options.
This research also suggests a new method for the estimation of stochastic volatility models, where estimation over a long horizon is likely to provide robustness not associated with current methods.

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Working Paper #67, May 2000 (Ini 2, Ini 6)

Pötzelberger, Sögner

Stochastic Equilibrium: Learning by Exponential Smoothing

This article considers three standard asset pricing models with adaptive agents and stochastic dividends. The models only differ in the parameters to be estimated. We assume that only limited information is used to construct estimators. Therefore, parameters are not estimated consistently. More precisely, we assume that the parameters are estimated by exponential smoothing, where past parameters are down-weighted and the weight of recent observations ddoes not decrease with time. This situation is familiar for applications in finance. Even if time series of volatile stocks or bonds are available for a long time, only recent data is used in the analysis. In this situation the prices do not converge and remain a random variable. This raises the question how to describe equilibrium behavior with stochastic prices. However, prices can reveal properties such as ergodicity, such that the law of the price process converges to a stationary law, which provides a natural and useful extension of the idea of equilibrium behavior of an economic system for a stochastic setup. It is this implied law of the price process that we investigate in this paper. We provide conditions for the ergodicity and analyze the stationary distribution.

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Working Paper #68, May 2000 (Ini 5)

Bullnheimer, Dawid, Reimann

To Innovate or Not To Innovate

In this paper we analyze the evolution of output decisions of adaptive firms in an environment of oligopolistic competition. The firm might either choose to produce one of several existing product variants or try to establish a new product variant on the market. The demand for each individual product variant is subject to a life-cycle, but aggregate demand for product variants is constant over time. Every period each firm has to decide whether to produce the product again, to introduce a new product variant itself (which generates an initial advantage on that market), or to follow another firm and change to the production of an already established product. Different firms have heterogeneous abilities to develop products respectively imitate existing designs, and therefore the effects of the decision whether to imitate existing designs or to innovate differ between firms. We examine the evolution of behavior in this market using an agent based simu-lation model. The firms are endowed with simple rules to estimate market potentials and market founding potentials of all firms including themselves, and make their decisions using a stochastic learning rule. Furthermore, the characteristics of the firms change dynamically due to 'learning by doing' effects. The main questions discussed are how the success and the optimal strategy of a firm depend on the interplay between characteristics of the industry and properties of the firm.

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Working Paper #69, May 2000 (Ini 6)

Sögner

Selection of the Number of States by Birth-Death Processes

In this article we use spatial birth-death processes to estimate the number of states $k$ of a switching model. Following Preston (1976) and Stephens (1998) matching the detailed balance condition for the underlying birth-death process results in an unique invariant probability measure with the corresponding stationary distribution of the number of states. This concept could be easily integrated to Bayesian sampling to derive the marginal posterior distribution of the number of states within the sampling procedure. We apply this technique to simulated $AR(1)$ data and to quarterly Austrian data on unemployment and real gross domestic product.

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Working Paper #70, July 2000 (Ini 5)

Markus Feurstein,  Martin Natter, Andreas Mild,  Alfred Taudes

Incentives to Cooperate in New Product Development

The knowledge required for decision making in a firm is distributed across various departments.  In practice cross functional teams are used to integrate this distributed knowledge. Incentive schemes are of crucial importance to encourage departments to share knowledge.
In this paper, we study different incentive schemes by means of a two stage model. In the first step departments have to choose between learning and sharing knowledge, in the second stage, they bargain about a new product feature. The outcome of the bargaining process in the second stage depends on the capabilities of the agents and their uncertainty about the opponent. The result of the second stage determines the agents' payoffs which in turn influence the time allocation. In a simulation study, we investigate different incentive systems and show to which extent a firm has to reward the sharing of knowledge in order to reach its overall objectives. Furthermore, we are able to derive an analytical solution for the bargaining process under uncertainty and compute Nash equilibria for a discrete set of possible actions.

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Working Paper #71, August 2000 (Ini 1)

Sara Dolnicar, Friedrich Leisch

Getting More Out of Binary Data: Segmenting Markets by Bagged Clustering

There are numerous ways of segmenting a market based on consumer survey data. We introduce bagged clustering as a new exploratory  approach in the field of market segmentation research which offers a  few major advantages over both hierarchical and partitioning   algorithms, especially when dealing with large binary data sets:  In the hierarchical step of the procedure the researcher is enabled  to inspect if cluster structure exists in the data and gain insight  about the number of clusters to extract. The bagged clustering  approach is not limited in terms of sample size, nor dimensionality  of the data. More stable clustering results are found than with   standard partitioning methods (the comparative evaluation is demonstrated for the $K$-means and the LVQ algorithm).  Finally, segment profiles for binary data can be depicted in a more informative way by visualizing bootstrap replications with box plot diagrams. The target audience for this paper thus consists of both academics and practitioners interested in explorative partitioning  techniques.

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Working Paper #72, August 2000 (Ini 5)

Thomas Fent

Wissen gewinnen und gewinnen durch Wissen

Gemäß Alfred Korzybski (1921) unterscheidet sich der Mensch von Pflanzen und Tieren unter anderem durch seine Eigenschaft als "Zeit-
Binder". Diese befähigt ihn, Erfahrung durch die Zeit zu transportieren. Menschen können Wissen aus der Vergangenheit ansammeln und
das, was sie wissen, der Zukunft mitteilen. In der vorliegenden Arbeit werden die Möglichkeiten und Grenzen untersucht, diese Fähigkeit durch Algorithmen zu beschreiben, und in künstlichen lernenden Systemen zu implementieren. Zur Illustration wird abschließend aufgezeigt, wie ein künstlicher Agent und seine Umgebung beschaffen sein können, um ihm das Erlernen einer erfolgreichen Strategie in einem einfachen Nimm-Spiel zu ermöglichen.

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Working Paper #73, September 2000 (Ini 6)

Andrea Gaunersdorfer, Cars H. Hommes, Florian O. O. Wagener

Bifurcation Routes to Volatility Clustering

A simple asset pricing model with two types of adaptively learning traders, fundamentalists and technical analysts, is studied. Fractions of these trader types, which are both boundedly rational, change over time according to evolutionary learning, with technical analysts conditioning their forecasting rule upon deviations from a benchmark fundamental. Volatility clustering arises endogenously in this model. Two mechanisms are proposed as an explanation. The first is coexistence of a stable steady state and a stable limit cycle, which arise as a consequence of a so-called Chenciner bifurcation of the system. The second is intermittency and associated bifurcation routes to strange attractors. Both phenomena are persistent and occur generically in nonlinear multi-agent evolutionary systems.

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Working Paper #74, September 2000 (Ini 6)

Andrea Gaunersdorfer

Adaptive Beliefs an the Volatility of Asset Prices

I present a simple model of an evolutionary financial market with heterogeneous agents, based on the concept of adaptive belief systems introduced by Brock and Hommes (1997a). Agents choose between different forecast rules based on past performance, resulting in an evolutionary dynamics across predictor choice coupled to the equilibrium dynamics. The model generates endogenous price fluctuations
with similar statistical properties as those observed in real return data, such as fat tails and volatility clustering. These similarities are demonstrated for data from the British, German, and Austrian stock market.

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Working Paper #75, Oktober 2000 (Ini 6)

Immanuel Bomze

Portfolio selection via replicator dynamics and projections of indefinite estimated covariances

Replicator dynamics are an increasingly popular device for obtaining (local) solutions of considerably high quality to so-called standard quadratic optimization problems, which consist of finding maxima of (possibly indefinite) quadratic forms over the standard simplex. In the
simplest version of portfolio selection, the quadratic form is theoretically negative-semidefinite, so that any local solution automatically is a global one. However, if it comes to more realistic set-ups, then (i) no market portfolio is available, so that one ends up with an indefinite theoretical problem; (ii) estimated covariance matrices modelling risk may be indefinite also. This paper deals with both problems in a different way: (i) will be solved via escape steps to avoid low-quality local solutions while (ii) is dealt with by several projection strategies which convert the indefinite estimated covariance matrix into a positive-semidefinite
one.

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Working Paper #76, November 2000 (Ini 5)

Karl Doerner, Richard Hartl, Marc Reimann

Ant Colony Optimization applied to the Pickup and Delivery Problem

 In this paper we propose an ACO algorithm to optimize the total costs associated with the pickup and delivery of full truckloads under time window constraints in a hub network. We perform a thorough technical analysis of the ACO by comparing different pheromone decoding schemes, different visibility information and various population sizes. Furthermore we propose a post-optimization technique to improve the solutions. Our results show that appropriate data structures significantly improve the solution quality.

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Working Paper #77, November 2000 (Ini 5)

Karl Doerner, Richard Hartl, Marc Reimann

Cooperative Ant Colonies for Optimizing Resource Allocation in Transportation

In this paper we propose an ACO approach, where two colonies of ants aim to optimize total costs in a transportation network. This main objective consists of two sub goals, namely fleet size minimization and minimization of the vehicle movement costs, which are conflicting for some regions of the solution space. Thus, our two ant colonies optimize one of these subgoals each and communicate information concerning solution quality. Our results show the potential of the proposed method.

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Working Paper #78, December 2000 (Ini 1)

Achim Zeileis

p Values and Alternative Boundaries for CUSUM Tests

Firstly rather accurate approximations to the p value functions of the common Standard CUSUM test and the OLS-based CUSUM test for structural change are derived. Secondly alternative boundaries for both tests are suggested and their properties are examined by simulation of expected p values. It turns out that the power of the OLS-based CUSUM test for early and late structural changes can be improved, whereas this weakness of the Standard CUSUM test cannot be repaired by the new boundaries.

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Latest Update: 19. Mär 02 by ML

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