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 ...

Abstract When heterogeneous players make strategic investment decisions in multi-stage contests, they might conserve resources a current contest to spend more subsequent contest, if the degree of heterogeneity (subsequent) is sufficiently large (small). We confirm these predictions using data from German professional soccer, which are subject one-match ban accumulate five yellow cards. Players ...

An investor has to carefully select the location and size of new generation units it intends build, since adding capacity in a market affects profit from this may already own. To capture closed-loop characteristic, strategic investment (SI) can be posed as bilevel optimization. By analytically studying small market, we first show that its objective function non-convex discontinuous. Realizing e...

In this paper we shall represent strategic planning problems by dynamic decision trees, in which the nodes are projects that can be deferred or postponed for a certain period of time. Using the theory of real options an enhanced option pricing method is provided, where the relationship of investments is taken into consideration as well, and the optimal path of the decision tree, i.e. the path w...

Viewing investment projects in new technologies as real options, this paper studies the effects of endogenous competition and asymmetric information on the strategic exercise of real options. We first develop a multi-period, game-theoretic model and show how competition leads to early exercise and aggressive investment behaviors and how competition erodes option values. We then relax the typica...

The transformation of the European energy system requires substantial investment in transmission capacity to facilitate cross-border trade and to efficiently integrate renewable energy sources. However, network planning in the EU is still mainly a national prerogative. In contrast to other studies aiming to identify the pan-European (continental) welfare-optimal transmission expansion, we inves...

As becomes apparent from the standard text books in industrial organization (cf. Tirole, 1988, The Theory of Industrial Organization), the analysis of the effects of uncertainty within this field is yet underdeveloped. This paper shows that the new theory of strategic real options can be used to fill this gap. Based on the work by Smets (1991) standard models are identified, and they are analyz...