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This paper derives put-call parity relations for barrier options via a probabilistic approach. As in the case of standard options, the difference between call and put prices depends on the stock price and the discounted exercise price. However, these terms now become functions of the moments of the relevant defective distributions and as such correct for the loss of probability that the barrier provisions bring. Moments are also useful building blocks for the valuation of a wide variety of time-depending rebate specifications that are interesting both from a theoretical as well as a practitioner’s point of view. For instance, rebate payments that are larger when the option is knocked out later recognize the higher opportunity costs caused by the option having immobilized funds over a longer period of time.

Since the 1950's economists applied game theoretical concepts to a wide variety of economic problems. The Nash equilibrium concept has proven to be a powerful instrument in analyzing the outcome of economic processes. Since the late 1980's economists also show a growing interest in the application of evolutionary game theory. This paper discusses the main concepts of evolutionarygame theory and their applicability to economic issues. Whereas traditional game theory focusses on the static Nash equilibria as the possible outcomes of the game, evolutionary game theory teaches us to model explictly the behavior of individuals outside equilibrium. This may provide us with a better understanding of the dynamic forces within a society of interacting individuals.

Recent research based on Dutch marriage records shows a steady decrease offemale labour force participation from the 1840s until the 1930s. However, this researchrelies on combined data from several municipalities. Analysing the sources in this wayaggregates the development to such an extent that local variation is completely overlooked.This article contributes to our understanding of regional variation in unmarried women’slabour from 1812 to 1932. The purpose of this research is to isolate the developments inindustry from those in agriculture and the service sector. I use marriage records from fourregions that list the occupation of the bride to determine the amount of working unmarriedwomen throughout the research period. My data show a different development from thepreviously mentioned research. Unlike earlier results, I found that unmarried women’s labourforce participation in the industrial centres did not decrease gradually throughout thenineteenth and early-twentieth century. Moreover, labour force participation was remarkablyhigh compared to the other sectors, especially during the first decades of the twentiethcentury. I argue that industry developed in a specific way because it required a cheap labourforce which was mostly found among young women. This statement is supported by showingthe percentages of brides with a recorded occupation in two industrial centres. Furthermore, Ishow that in these centres, the younger a woman was, the higher the chance that she stated anoccupation in her marriage record. This was not the case in the agricultural and serviceorientedregions I have investigated. I therefore argue that research on the history of femalelabour should be approached from a comparative perspective for a proper understanding of itsdevelopments.

Given the assumption that the components of a vector time series are stationary about nonlinear deterministic time trends, nonlinear co-trending is the phenomenon that one or more linear combinations of the time series are stationary about a linear trend, hence the series have common nonlinear deterministic time trends.In this paper we shall develop nonparametric tests for nonlinear co-trending.The tests are based on generalized eigenvalues, where the two matrices involved are constructed nonparametrically on the basis of partial sums.We apply this approach to the federal funds rate and the CPI inflation rate in the U.S., using monthly data.It appears that these series are nonlinearly co-trended, where the nonlinear trend in the inflation rate is positively related to the nonlinear trend in the interest rate.This positive relation between interest and inflation is known in the literature as the price puzzle. Thus, our result suggests that the price puzzle is due to a common nonlinear time trend in the series involved.

In this paper we discuss the issue of primary and secondary actions to direct mail offers. Primary action refers to the first responses consumers make toward a direct offer or soliciation. It might represent an order for a product, a request for a catalog or credit card, or a pledge to donate to a charity. As little money changes hands on primary actions, companies are also interested in secondary actions, i.e., bad debts, returns, or payments. A company concentrating solely on the prediction of primary actions might lose money on customers who do not ultimately pay. We present a model which jointly models primary and secondary action and incorporates the correlation between the two action probabilities. We also show how optimal selection should take place incorporating predicted primary and secondary action jointly. In an empirical study, the new joint model yields superior profits when compared to a split model assuming the independence of primary and secondary actions. Keywords: Database marketing, bivariate probit

AMS classifications: 90D12; 90C05; 90C34;

This paper investigates whether ECB corporate sector purchases impact the funding structure of non-financial corporates. Regression models are estimated using a unique microdata panel, combining data on all Eurosystem corporate sector purchases and individual balance sheets of 672 non-financial corporations headquartered in the euro area with access to capital markets. The findings indicate that ECB purchases of corporate bonds reduce the dependence on bank financing of corporates whose debt is purchased. The effects vary according to corporates interest paid, financial expenses and price-to-book ratio. In addition, this paper shows that the relationship between central bank purchases and corporates dependence on bank financing is non-linear. The downward effect on bank dependence is largest for those corporates of which most debt is purchased under the CSPP, relative to their total stock of debt.

The Kolmogorov axioms for probability functions are placed in the context of signed meadows. A completeness theorem is stated and proven for the resulting equational theory of probability calculus. Elementary definitions of probability theory are restated in this framework.