Modifying the proof of a theorem of Wilkie, it is shown that if a one dimnsional set S is definable in an O minimal expansion of the ordered field of the reals, and if it is regularly exponentially near to many integral points, then there is an unbounded set, which is R definable without parameters, and which is exponentially near to S.

In this article we will describe some of the main developments in interest-rate modelling since Black & Scholes’ (1973) and Merton’s (1973) original articles on the pricing of equity derivatives. In particular, we will focus on continuoustime, arbitrage-free models for the full term structure of interest rates. Other models which model a limited number of key interest rates or which operate in ...

The paper considers a model of a federation with two heterogeneous regions that try to attract the capital by competing in capital income taxes and public investment that enhance the productivity of capital. The regions’ choices determine the allocation of capital across the regions and their revenues under a tax sharing scheme. This framework allows for the examination of different approaches ...

Battles for corporate control have increasingly attracted the public spotlight. This attention reflects not only the growth in the number of acquisitions in the 1980s but also the size of the targets. Firms previously thought too large to be takeover targets have been acquired despite active management opposition. Any acquisition, and particularly one involving sizable assets, is likely to resu...

t Wilkie's stochastic investment model and its variants have been increasingly applied by actuaries around the world to actuarial modeling and simulation. This paper performs time series outlier analysis on retail price inflation, which is the driving force of Wilkie's composite model. The data come from four developed countries: the United Kingdom, the United States, Canada, and Australia. The...

Within the public sector domain there is great potential for business process optimization through ICT. However, until today these possibilities remain largely unexploited. To measure the impact of ICT-investments all processes of a public administration have to be taken into account. The PICTURE modelling method has been proposed as a way to efficiently model the whole process landscape of a p...