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In this paper we investigate the use of mixture density networks (MDNs) for identifying complex stochastic processes. Regular multilayer perceptrons (MLPs), widely used in time series processing, assume a gaussian conditional noise distribution with constant variance, which is unrealistic in many applications, such as financial time series (which are known to be heteroskedastic). MDNs extend this concept to the modeling of time-varying probability density functions (pdfs) describing the noise as a mixture of gaussians, the parameters of which depend on the input. We apply this method to identifying the process underlying daily ATX (Austrian stock exchange index) data. The results indicate that MDNs modeling a non-gaussian conditional pdf tend to be significantly better than traditional linear methods of estimating variance (ARCH) and also better than merely assuming a conditional gaussian distribution. (author's abstract), Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Despite the lack of a precise definition of volatility in finance, the estimation of volatility and its prediction is an important problem. In this paper we compare the performance of standard volatility models and the performance of a class of neural models, i.e. mixture density networks (MDNs). First experimental results indicate the importance of long-term memory of the models as well as the benefit of using non-gaussian probability densities for practical applications. (author's abstract)

Das Konzept Value at Risk (VaR) scheint sich als Standard im Rahmen von internen Risikomanagementmodellen in der Praxis durchzusetzen. Als quantitatives Risikomaß setzt es sich aus einem Volatilitätsmaß, der Modellierung von Verteilungen von Wertpapierrenditen und einem Bewertungsmodell zusammen. Die vorliegende Arbeit untersucht nun empirisch welche Bedeutung diese Komponenten für den VaR eines einfachen Aktienportefeuilles haben. Dabei zeigt sich, daß die Wahl des Volatilitätsmaßes keinen signifikanten Einfluß auf die Ermittlung des VaR für ein Aktienportefeuille hat. Sowohl die Annahme über die Verteilung der Aktienrenditen als auch der Bewertungsansatz mit dem das Aktienportefeuille abgebildet wird, können gravierende Änderungen im VaR nach sich ziehen. Diese Ergebnis läßt daher den Schluß zu, daß bei der Ermittlung der Eigenkapitalvorsorge im Rahmen der Kapitaladäquanzrichtlinie die Wahl des geeigneten Bewertungsmodells als auch der Verteilungsfunktion von großer Bedeutung sind. (Autorenreferat), Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

We consider a market in which a single supplier sells a new product characterized by diffusion effects on the demand side. In this setting we analyze the problem whether or not the government should subsidize the diffusion of this innovation. We assume that the government is a Stackelberg leader and decides about the subsidy (price or cost subsidy) before the supplier sets his optimal price. The objective of the government is to choose a subsidy policy such that the number of adopters at the horizon date is maximized. The firm chooses a pricing strategy so as to maximize the present value of profits.

It is well known that non-cooperative behaviour of different policy-makers, either central bank and government on a national level or governments of different countries on an international level, may result in severe overall losses and inefficiencies. On the other hand, policy coordination is difficult to achieve, given the mechanisms of negotiations between several policy-making institutions. A solution to this “trade-off” would be a mechanism inducing individual behaviour that ensures efficient (Pareto-optimal) outcomes equivalent to those achieved by cooperation, but without the need of explicit agreements.

Publisher Summary This chapter discusses the solutions for a general class of capital accumulation games with stability properties of Nash equilibrium. It focuses on the application of turnpike theory to dynamic games. The turnpike results known from the theory of optimal economic growth can be used to derive a general convergence result. They also yield comparative statics and dynamics properties. The key result is the global convergence of the Nash trajectories to a unique steady state provided that the matrix of second order derivatives of the profit functions has a dominant diagonal. This result implies that the block diagonal assumption introduced by Araujo and Scheinkman is satisfied. Thus, comparative statics and dynamics analyses are possible. The chapter presents a model, which is very general in nature and can be applied to various market situations. The chapter discusses the relationship between the equilibrium path of the finite and infinite-horizon games. The finite horizon eqilibrium path stays within a closed neighborhood of the stationary equilibrium.

Series: Department of Economics Working Paper Series

Series: Department of Economics Working Paper Series

Series: Department of Economics Working Paper Series

"In this paper we attempt to explain the occurrence of population cycles in industrialised economies where the birth rate depends on the difference between the actual and the expected consumption rate. This model of an endogenously growing population brings together Easterlin's idea of an adapting aspiration level with the neoclassical optimal growth paradigm. It is shown that in this highly aggregated demo-economic system (i.e., without inclusion of the age structure of a population) swings both in the economic and demographic variables may exist. The reason behind this 'strange' optimal behaviour is identified to be an intertemporal substitution effect between current and future levels of consumption."

For a general linear-quadratic differential game model of macroeconomic policies with two policy-makers, we derive no-memory non-cooperative feedback Nash equilibrium strategies and Pareto-optimal strategies. Since the non-cooperative equilibrium solution in general is inefficient, policy coordination provides advantages but may not be sustainable, if only memoryless strategies are considered. However, if memory strategies are admitted, then there may exist subgame-perfect efficient noncooperative equilibrium solutions, and efficient stabilization policies may be achieved without policy coordination.

This paper studies the strategic implications of price-advertising interactions in an intertemporal setting. Our model is based on three dynamic effects: product life cycle, learning by doing, and discounting. The main interest lies on the interaction between the optimal price and advertising policies and their dependence on the product life cycle. As a general result it turns out that the optimal price policy follows the product life cycle. Moreover, both the advertising and the pricing policies do depend on the efficiency of advertising expenditures.

This paper explores the relationship between dynamic oligopolistic competition and static conjectural variations equilibria. Using an infinite horizon adjustment cost model, the author demonstrates that any steady state closed-loop (subgame-perfect) equilibrium coincides with a conjectural variations equilibrium. In the case of linear demand and quadratic costs, the dynamic conjectures consistent with closed-loop steady state equilibria are negative, constant, symmetric, and vary continuously with the discount rate (and the adjustment cost parameter) in an interval between the static consistent conjectures and zero (Cournot). Copyright 1992 by Blackwell Publishing Ltd.

This paper examines the effects of voluntary export restraints in a dynamic game model of duopolistic competition. It is shown that the imposition of a voluntary export restraint at the free-trade level of imports increases the market price and the profits of all firms in the industry if free trade is identified as the closed-loop (subgame-perfect) Cournot equilibrium of the game. Hence, the authors conclude that the predictions of static Cournot competition do not carry over to the dynamic case.

In 1977, Lieber and Barnea presented an investment and pricing differential game. There are two players, a monopoly possessing some exhaustible resource and a price-taking competitor. The monopoly wishes to determine an optimal price, whereas the competitor wishes to choose optimal investment in an alternative production. This paper presents a non-linear extension of the game. The special structure of the game permits a complete solution in the state—costate phase plane as well as in the control phase plane. The monopoly plays an optimal decreasing price strategy and the competitor plays an optimal decreasing investment strategy with an increasing production capacity.

Stabilization policy is modeled as a linear-quadratic differential game between government and central bank aiming at a reduction of unemployment and inflation with different weights attached to these targets. We derive non-cooperative open-loop Nash equilibrium strategies for both players, showing them to be constant, subgame perfect (feedback Nash equilibrium strategies), and simultaneously Stackelberg equilibrium strategies with either player as the leader. For the same game, cooperative Pareto-optimal strategies are derived, also resulting in constant controls to be interpreted as fixed policy “rules”. It is shown that non-cooperative outcomes in general do not belong to Pareto-optimal ones and therefore are inefficient.

In this note we study conditions under which non-cooperative open-loop multi-agent resource extraction of a natural resource results in efficient (Pareto-optimal) extraction policies. Previous results presented in the literature are extended to include undiscounted resource utilization.

Summary In this paper we consider a dynamic oligopolistic model where the demand curve is described by a first—order differential equation which relates at each point in time the price of the commodity, the rate of change of the price, and the outputs of all firms in the market. The linear dynamic demand equation is considered as a first—order price adjustment mechanism. Open—loop, feedback and closed—loop Nash equilibria are derived. The corresponding stationary solutions are compared to the static Cournot equilibrium price and the competitive equilibrium price. It is demonstrated that for the “limiting game” (when the constant speed of adjustment reaches infinity) only the stationary open—loop price converges to the static Cournot price. The stationary feedback and a particular closed—loop solution converge to a price which is below the static Cournot price. For the limiting game when the number of firms goes to infinity the Nash equilibrium prices (independent of the information structure assumed) converge to the long—run competitive equilibrium.

The purpose of the paper is to determine the behavior of Nash optimal open-loop advertising strategies of a dynamic duopoly. The logarithmic two-person nonzero-sum advertising differential game analyzed byJorgensen [1982] is extended to more general nonlinear functionsg (u1,u2) measuring the effectiveness of advertising expendituresu1,u2 of two firms with respect to the development of the market shares over time. It is shown that under the assumption of zero cross effects of the advertising efficiency function the main features of Jorgensen's model are preserved. Furthermore, two models with advertising rates interacting asymmetrically with respect to the marginal advertising effectiveness are studied. For zero salvage values of terminal market shares it is shown that the Nash optimal advertising expenditures of a small firm are always downward sloping, whereas the shape of a large competitor's advertising rate can only be determined under additional assumptions.

The polarographic reduction of low molecular and high molecular N-chlorocarboxamides at the dropping mercury electrode proceeds in two one-electron-transfer steps, which are highly irreversible. In the case of the low molecular models 1 and 2 the reaction is diffusion-controlled, whereas in the case of the poly(N-chloroamide) 3 the reaction is adsorption-controlled. Reduction of several poly(N-chloroamide)s shows always two reduction waves with a distance of 0,5 V. There is, however, no relation between the polyamide-type and the position of the half-wave potentials. The polarographic reduction can be used as an analytical method for quantitative determination of N-chlorocarboxamide groups in polymers.

On irradiating poly(N-chloroamide)s in films or in solution in the range of 325–375 nm carboxamide groups are formed. The irradiated polymer contains chlorine which is linked to C-atoms. This reaction can certainly not be explained with an intramolecular photorearrangement but with a sequence of photoreactions and dark reactions satisfactorily accounting for all observations.

(S)-Poly(2-aminobutyric acid) (1) [(S)-poly(imino-1-methyl-3-oxotrimethylene)] was transformed into its N-trifluoroacetyl derivative 4. The IR spectra and the circular dichroism of both substances were compared. In addition, (S)-poly[N-(1-phenylethyl)acrylamide] (2) ((S)-poly-[1-(1-phenylethylaminocarbonyl)ethylene]) was trifluoroacetylated leading to polymer 5. 4 was found to react as trifluoroacetylating agent with L-1-phenylethylamine (L-3) twice as fast as it reacts with D-3. Accordingly, the reaction of 4 with D,L-3 leads preferentially to the L-form of N-(1-phenylethyl)trifluoroacetamide with optical yields up to 6%. The reaction of 5 with D,L-3 affords the D-form of N-(1-phenylethyl)trifluorcacetamide with optical yields up to 13%.

For a general linear-quadratic differential game model of macroeconomic policies with two policy-makers, we derive no-memory non-cooperative feedback Nash equilibrium strategies and Pareto-optimal strategies. Since the non-cooperative equilibrium solution in general is inefficient, policy coordination provides advantages but may not be sustainable, if only memoryless strategies are considered. However, if memory strategies are admitted, then there may exist subgame-perfect efficient noncooperative equilibrium solutions, and efficient stabilization policies may be achieved without policy coordination.