Perfect Competition in an Oligoply (including Bilateral Monopoly)

We show that if limit orders are required to vary smoothly, then strategic (Nash) equilibria of the double auction mechanism yield competitive (Walras) allocations. It is not necessary to have competitors on any side of any market: smooth trading is a substitute for price wars. In particular, Nash equilibria are Walrasian even in a bilateral monopoly.Limit orders, double auction, Nash equilibria, Walras equilibria, mechanism design

Towards Optimal Degree-distributions for Left-perfect Matchings in Random Bipartite Graphs

Consider a random bipartite multigraph $G$ with $n$ left nodes and $m \geq n \geq 2$ right nodes. Each left node $x$ has $d_x \geq 1$ random right neighbors. The average left degree $\Delta$ is fixed, $\Delta \geq 2$. We ask whether for the probability that $G$ has a left-perfect matching it is advantageous not to fix $d_x$ for each left node $x$ but rather choose it at random according to some (cleverly chosen) distribution. We show the following, provided that the degrees of the left nodes are independent: If $\Delta$ is an integer then it is optimal to use a fixed degree of $\Delta$ for all left nodes. If $\Delta$ is non-integral then an optimal degree-distribution has the property that each left node $x$ has two possible degrees, \floor{\Delta} and \ceil{\Delta}, with probability $p_x$ and $1-p_x$, respectively, where $p_x$ is from the closed interval $[0,1]$ and the average over all $p_x$ equals \ceil{\Delta}-\Delta. Furthermore, if $n=c\cdot m$ and $\Delta>2$ is constant, then each distribution of the left degrees that meets the conditions above determines the same threshold $c^*(\Delta)$ that has the following property as $n$ goes to infinity: If $c<c^*(\Delta)$ then there exists a left-perfect matching with high probability. If $c>c^*(\Delta)$ then there exists no left-perfect matching with high probability. The threshold $c^*(\Delta)$ is the same as the known threshold for offline $k$-ary cuckoo hashing for integral or non-integral $k=\Delta$

On partial defaults in portfolio credit risk: Comparing economic and regulatory view

Most credit portfolio models calculate the loss distribution of a portfolio consisting solely of performing counterparts. We develop two models that account for defaulted counterparts in the calculation of the economic capital. First, we model the portfolio of non-performing counterparts standalone. The second approach derives the integrated loss distribution for the non-performing and the performing portfolio. Both calculations are supplemented by formulae for contributions of the single counterpart to the economic capital. Calibrating the models allows for an impact study and a comparison with Basel II. --

On Partial Defaults in Portfolio Credit Risk : A Poisson Mixture Model Approach

Most credit portfolio models exclusively calculate the loss distribution for a portfolio of performing counterparts. Conservative default definitions cause considerable insecurity about the loss for a long time after the default. We present three approaches to account for defaulted counterparts in the calculation of the economic capital. Two of the approaches are based on the Poisson mixture model CreditRisk+ and derive a loss distribution for an integrated portfolio. The third method treats the portfolio of non-performing exposure separately. All three calculations are supplemented by formulae for contributions of the counterpart to the economic capital. --Portfolio credit risk,CreditRisk+,Recovery

Urban Design for Mussolini, Stalin, Salazar, Hitler and Franco During the Interwar Period

Urban design played a central role for the European dictatorships during the 20th century, it served to legitimate the regime, to produce agreement, to demonstrate power, efficiency and speed, it communicated the social, as well as design projects, of the dictatorial regimes domestically and internationally, it tied old experts, as well as new, to the regime. Dictatorial urban design also played an important role after the fall of the dictatorships: It became the object of structural and verbal handling strategies: of demolition, of transformation, of reconstruction, of forgetting, of suppressing, of re-interpretation and of glorification. The topic area is, therefore, both historical and relevant to the present day. The discussion of the topic area is, like it or not, always embedded in the present state of societal engagement with dictatorships. In order to even be able to discuss all of these aspects, different conceptual decisions are necessary. In retrospect, these may seem to many as self-evident, although they are anything but. Our thesis is that there are three methodological imperatives, especially, which allow an expanded approach to the topic area “urban design and dictatorship”. First and above all, the tunnel view, focused on individual dictatorships and neglecting the international dimension, must be overcome. Second, the differences in urban design over the course of a dictatorship, through an appropriate periodisation, should be emphasised. Third, we must strive for an open, flexible, but complex concept of urban design. The main focus lies on the urban design of the most influential dictatorships of the first half of the 20th century: Soviet Union, Fascist Italy and Nazi Germany, including the urban design of the autarky periods in Portugal and Spain. After all, urban design is not just a product of specific historic circumstances. It is a form that continues to have long-term effects, which demonstrates its usefulness and adaptability throughout this process. The urban design products undoubtedly still recall the dictatorial rule under which they were created. However, they are more than a memory space. They are also a living space of the present. They can and should be discussed with respect to their spatial and functional utility for today and tomorrow. Such a perspective is a given for the citizens of a city, but also for city marketing, having marvellous consequences. Only when we do not exclude this dimension a priori, even in academic discussions, can we do justice to the products of dictatorships. And finally, the view of the urban design of dictatorships can and must contribute to the questioning of simplified and naive conceptions of dictatorships. With urban design in mind, we can observe how dictatorships work and how they were able to prevail. In Europe, these questions are of the highest actuality

Enlarged infarct volume and loss of BDNF mRNA induction following brain ischemia in mice lacking FGF-2

FGF-2, a potent multifunctional and neurotrophic growth factor, is widely expressed in the brain and upregulated in cerebral ischemia. Previous studies have shown that intraventricularly or systemically administered FGF-2 reduces the size of cerebral infarcts. Whether endogenous FGF-2 is beneficial for the outcome of cerebral ischemia has not been investigated. We have used mice with a null mutation of the fgf2 gene to explore the relevance of endogenous FGF-2 in brain ischemia. Focal cerebral ischemia was produced by occlusion of the middle cerebral artery (MCAO). We found a 75% increase in infarct volume in fgf2 knock-out mice versus wild type littermates (P < 0.05). This difference in the extent of ischemic damage was observed after 24 h, and correlated with decreased viability in fgf2 mutant mice following MCA occlusion. Increased infarct volume in fgf2 null mice was associated with a loss of induction in hippocampal BDNF and trkB mRNA expression. These findings indicate that signaling through trkB may contribute to ameliorating brain damage following ischemia and that bdnf and trkB may be target genes of FGF-2. Together, our data provide the first evidence that endogenous FGF-2 is important in coping with ischemic brain damage suggesting fgf2 as one crucial target gene for new therapeutic strategies in brain ischemia