We consider a linear-quadratic differential game with two decision makers which is interpreted as a model of the interactions between the government and the private sector. The open-loop Stackelberg equilibrium solution of this game is determined analytically. We then formulate a linear dynamic continuous-time model with rational expectations. We show that under some assumptions, the problem of determining optimal policies for a government with an economy given by the rational-expectations model is equivalent to the problem of determining the leader’s open-loop Stackelberg equilibrium strategy for the differential game. Consequences are briefly discussed for the time inconsistency of optimal policies and for the problem of the non-uniqueness of the solutions of rational-expectations models.

The paper considers the problem of an investor that has the option to acquire a firm. Initially this firm is run as to maximize shareholder value, where the shareholders are risk averse. To do so it has to decide each time on investment and dividend levels. The firm’s capital stock can be financed by equity and debt, where less solvable firms pay a higher interest rate on debt. Revenue is stochastic.

The paper extends the Lanchester model of advertising competition to a setup in which the rate at which a firm attracts customers from its competitors depends not only on the firm’s own advertising effort, but also on the efforts of its rivals. Doing so enables us to use attraction rate specifications borrowed from the economic theory of contests. Exploiting the fact that the sum of attraction rates equals one, we show that the differential equations that define the evolution of market shares in the Lanchester model can be considerably simplified. This makes the optimization problems of the firms considerably easier to analyze. Finallly, to illustrate how the above extensions work, three alternative specifications of attraction rates are studied: the Tullock ratio formulation, a linear transformation of the Tullock ratio, and a specification that incorporates an exogenous bias.

In a seminal paper Brander and Lewis (Am Econ Rev 76:956–970, 1986 ) show that oligopolistic firms with limited liability follow a more aggressive output strategy as their leverage increases. In a follow-up paper Glazer (J Econ Theory 62:428–443, 1994 ) points out that when debt is long term and rival firms choose their equilibrium quantities in two consecutive periods, they have an incentive to be more collusive in the first period than static oligopolists would be. In this paper we argue that the incentive to collude is driven by limited liability and the dividend policy of the firm. We find that increasing leverage causes firms in both periods to increase their output and hence to be more aggressive. Additionally, we find that it is always optimal to pay out profits immediately. Moreover, we show that the symmetric game admits multiple equilibria some of which cause firms to choose asymmetric product market strategies.

We analyze in a dynamic model how debt priority rules influence firms' initial capital structure choice, investment timing, and subsequent debt issues. We quantify deviations from first-best investment behavior that arise from different debt priority rules, and document surprisingly large deviations caused by well-known rules such as the absolute priority rule. We introduce a new rule, called the efficient priority rule (EPR), that gives equity holders incentives to choose first-best investment timing and financing. Under EPR, old debt has the same value and risk characteristics as if the firm had not invested and new debt had not been issued.

This paper studies investment in intellectual capital and corresponding value and risk dynamics over the innovation cycle. We assume that the innovation cycle consists of three phases, R&D, trial, and market introduction phases. We use a real option investment model to characterize firm value and risk dynamics over the innovation cycle and find that firm value is the sum of the value of assets in place and non-linear option values related to breakthrough, exit, and market introduction options. Firm risk over the innovation cycle is highly non-linear and quite distinct in different phases. During the R&D phase risk is high as the firm faces high operating leverage originating from R&D fixed costs together with technological uncertainty. During the trial phase risk is significantly lower and dominated by option risk to launch the product in the market while after the introduction of the product in the market risk is equivalent to the asset risk of the company. Our model is consistent with the view that positive excess returns of R&D intensive firms are a compensation for risk. Based on this insight we derive several testable predictions.

Standard option-based approximations for convenience yields make use of the assumption that commodity spot prices follow a geometric Brownian motion. While there is some empirical support for this assumption, prices of a wide variety of (agricultural) commodities mean revert. Using a mean-reverting spot price process we derive a novel convenience yield approximation analytically. It corresponds to the difference between the present values of two floating-strike Asian options written on the spot and the futures prices, respectively. Using natural gas spot and futures price data from four different trading locations, we compare convenience yield estimates derived from existing approximations to those of our new measure. We find that convenience yield estimates vary substantially across approximation methods and that differences can be attributed to the cost of carry and the moneyness of the options. (c) 2014 Wiley Periodicals, Inc. Jrl Fut Mark 35:625-654, 2015

Rivalry restraint has received a lot of attention as a theory of profits in recent research on business strategy. Its economic rationale is explained as the consequences of either exogenous or endogenous anticompetitive forces present in different industries. In this paper, we use a dynamic oligopolistic industry model and show that rivalry restraint emerges as equilibrium behavior among firm owners who delegate decisions to managers. In the corresponding two-stage game, managers choose optimal production rates in a dynamic Cournot market and owners set incentives for managers, acting sequentially rational. Equilibrium incentives correspond to rivalry restraint, that is, managers are less aggressive in the product market with lower outputs and increasing profits for all firms in the industry.

Accurate rating systems are of central importance for banks to price and manage their loan portfolios. A bank's choice to invest in a more accurate rating technology is based on a trade-off: the better rating system usually comes at higher cost, but endows the bank with a competitive advantage, which includes potentially better access to funds. This paper models the rating technology choice of a bank as a two-stage game in an oligopolistic banking sector. In the first stage banks choose between two alternative rating technologies that provide estimates about a borrower's default probability with varying precision. In the second stage banks set their loan prices based on estimated default probabilities in an imperfectly competitive loan market. While rating technology investment is lumpy and characterized by fixed costs, loan prices vary continuously with their markup over the risk-free rate of interest. The interaction of loan pricing and rating technology investment gives rise to the following predictions: equilibrium adoption of the new rating technology need not increase individual banks' profits; identical banks in a symmetric banking sector might adopt the more accurate rating technologies sequentially rather than simultaneously; and increased competition in the banking sector slows investment in the new rating technology.

Decentralized decision making is a fact in the modern business world accompanied by extensive research that looks into its consequences for overall firm profits. We study the interactions of decentralized marketing and operations divisions in a corporation and explore their impact on overall firm profits in the case with and without coordination of the two decentralized units. We assume that the marketing department is responsible for the price that influences the demand (sales), and the operations department is responsible for the production rate. We allow for backlogging over time. We model the interdependence involving marketing and operations decisions as a non‐cooperative differential game, with the two divisions as strategically interacting players. We find that, without coordination, strategic interactions of marketing and production result in inefficiencies that can quantitatively be substantial. Next, we introduce a dynamic transfer pricing scheme as a coordination device and evaluate if it establishes efficient (first best and fully coordinated) outcomes. We show that if production and marketing play a game with pre‐commitment strategies, there exists a dynamic transfer price that efficiently (fully) coordinates decentralized decision making and hence results in Pareto‐efficient company profits. If the two decentralized divisions play a game without pre‐commitment, dynamic transfer prices can partially coordinate decentralized decision making but fail to fully eliminate overall inefficiencies arising from strategic interactions among decentralized divisions.

Many economic problems can be formulated as dynamic games in which strategically interacting agents choose actions that determine the current and future levels of a single capital stock. We study necessary as well as sufficient conditions that allow us to characterise Markov-perfect Nash equilibria for these games. These conditions can be translated into an auxiliary system of ordinary differential equations that helps us to explore stability, continuity and differentiability of these equilibria. The techniques are used to derive detailed properties of Markov-perfect Nash equilibria for several games including voluntary investment in a public capital stock, the inter-temporal consumption of a reproductive asset, and the pollution of a shallow lake.

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We study the distinct impacts of own and rival actions on risk and return when firms strategically compete in the product market. Contrary to simple intuition, a competitor’s options to adjust capacity reduce own-firm risk. For example, if a rival possesses a growth option, an increase in industry demand directly enhances profits but also encourages value-reducing competitor expansion. The rival option thus acts as a natural hedge. Within the industry, we obtain endogenous differences in expected returns. In a leader-follower equilibrium, own-firm and competitor risks and required returns move together through contractions and oppositely during expansions, providing testable new predictions.

With the liberalization of energy markets integrated energy companies have separated into entities that specialize in production and/or transmission of energy. Transmission of energy requires balancing the grid to guarantee system security, which is performed by the (independent) system operator (SO). When the SO faces stochastic demand, grid balancing has sizeable consequences on current and future profits, and hence, on firm value and firm risk. We explore these value and risk consequences with and without an investment option to expand transmission capacity. We show that firm value consists of the value of the transmission capacity in place plus the value of a short put and a short call option that are the result of the SO's balancing actions. Firm risk without investment option is non-linear and determined by the short option positions. It is decreasing with increasing energy demand. The existence of an option to expand transmission capacity increases firm value and firm risk.

Credit risk has become an important factor driving government bond returns. We therefore introduce an asset pricing model which exploits information contained in both forward interest rates and forward CDS spreads. Our empirical analysis covers euro-zone countries with German government bonds as credit risk-free assets. We construct a market factor from the first three principal components of the German forward curve as well as a common and a country-specific credit factor from the principal components of the forward CDS curves. We find that predictability of risk premiums of sovereign euro-zone bonds improves substantially if the market factor is augmented by a common and an orthogonal country-specific credit factor. While the common credit factor is significant for most countries in the sample, the country-specific factor is significant mainly for peripheral euro-zone countries. Finally, we find that during the current crisis period, market and credit risk premiums of government bonds are negative over long subintervals, a finding that we attribute to the presence of financial repression in euro-zone countries.

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.

We consider a firm that employs human capital to make a technological breakthrough. Since the probability of success of the breakthrough depends on the current stock of human capital the firm has an incentive to expand its human capital stock. The present value of the patent is stochastic but can be observed during the R&D phase of the project. The exogenous value of the patent determines the firm’s decisions to invest in human capital, to abandon the project if necessary, and to invest in marketing the new product. We study the corresponding optimal stopping times, determine their value and risk consequences, and derive optimal investment in the stock of human capital. While optimal investment in human capital is very sensitive to its productivity do increase the probability of a breakthrough it is insensitive to changes in the volatility of the present value of the patent. The value of the firm is driven by fixed labor costs that occur until the breakthrough is made, the call option to invest in human capital and market the product, and the put option to abandon the project. These options together with labor costs’ based operating leverage determine the risk dynamics. Firm risk is inverse U-shaped and critically depends on the option to increase the stock of human capital, operating leverage arising from labor costs and the option to shut down if patent values are unattractive. Heiligenstaedter Strasse 46, 1190 Vienna, Austria, e-mail:engelbert.dockner@wu.ac.at, Tel: 0043 1 313366302 Fuglesangs Alle 4, 8210 Aarhus-V, Denmark, e-mail:barans@asb.dk, Tel: 0045 89486375 1

We consider an oligopolistic product market in which two competing firms instead of paying a competitive input price choose a two-part tariff. Costs for the input are divided up into upfront fixed costs independent of the output level and reductions in marginal costs. We explore under which competitive settings will such a two-part cost structure correspond to equilibrium behavior in a two stage game. We find that firms in a static model do have an incentive to choose a two-part cost structure when competition in the product market is not too strong and oligopoly rents can be shifted form the rival to the own firm. In a dynamic market when firms use Markov strategies competition is so intense that there are no rents to be shifted and firms do not benefit from two-part cost structures.

With this paper, dedicated to Gustav Feichtinger on the occasion of his 70th anniversary, the authors—all being his former students and/or collaborators—want to summarize and honor his remarkable scientific contributions and academic activities, and wish him many years of a further active and fruitful life. Gustav studied mathematics and physics at the University of Vienna (1958–1963), completed his PhD in algebra in 1963, worked for a year at the IBM research laboratory in Vienna, and continued his academic career as assistant and associate professor at the University of Bonn (1965–1972), where he also received his habilitation in statistics. In 1972 he became full professor of operations research at the TU Vienna