A NOTE ON ARBITRAGE AND CLOSED CONVEX CONES

We give an example of a subspace K of     such that     , where     denotes the closure with respect to convergence in probablity. On the other hand, the cone   C ≔ K − L ^∞₊  is dense in   L ^∞  with respect to the weak-star topology  σ( L ^∞, L ¹)  . This example answers a question raised by I. Evstigneev. The topic is motivated by the relation of the notion of no arbitrage and the existence of martingale measures in Mathematical Finance.     

The Asset Management Industry in Asia: Dynamics of Growth,Structure, and Performance

We examine the industrial organization and institutional development of the asset management industry in Asian developing economies—specifically in China, Indonesia, Korea, Malaysia, Singapore, Philippines, and Thailand. We focus on the size and growth of the buy‐side of the respective financial markets, asset allocation, the regulatory environment, and the state of internationalization of the fund management industry in its key components—mutual funds, pension funds, and asset management for high net worth individuals. We link the evolution of professional asset management in these environments to the development of the respective capital markets and to the evolution of corporate governance. We find that the fund management industry occupies a very small niche in domestic financial systems that are dominated by banks. At the same time, we find that its growth has been very rapid in the early 2000s and we suggest that this is likely to persist as the demand for professional management of financial wealth in the region develops and as the pension fund sectors of the respective economies are liberalized to allow larger portions of assets to be invested in collective investment schemes.     

Cardinality-based equality of opportunities

We study possible rankings of opportunity profiles. An opportunity profile is a list of opportunity sets, one for each agent in the society. We compare profiles on the basis of the notion of “equality of opportunities”. Our main results show the necessary and sufficient conditions for this comparison to be made using exclusively the information provided by two cardinal measures: the number of common alternatives in all sets of a given profile and the difference between the number of alternatives in the individual sets. We also show that, under additional axioms, we can combine these criteria only in a weighted procedure or in some lexicographic refinements of a weighted procedure.      

Building Small City and Town Sams and CGE Models

In this paper we attempt to describe both the data sources and organizational methods that allow for effective and easily created SAMs and regional computable general equilibrium (CGE) models. Small cities of around 100,000 people will face very different constraints than a town of 2000 people. Unfortunately, most CGE models typically describe relatively large geographical areas and are therefore not able to capture the uniqueness of individual cities within the region. An illustrative example using these methods demonstrates that the economic impacts vary substantially over different municipalities to the same economic shock.     

Habilitation von Ralf Hohlfeld

Ohne Zusammenfassung     

A Nonstandard Approach to Option Pricing

Nonstandard probability theory and stochastic analysis, as developed by Loeb, Anderson, and Keisler, has the attractive feature that it allows one to exploit combinatorial aspects of a well-understood discrete theory in a continuous setting. We illustrate this with an example taken from financial economics: a nonstandard construction of the well-known Black-Scholes option pricing model allows us to view the resulting object at the same time as both (the hyperfinite version of) the binomial Cox-Ross-Rubinstein model (that is, a hyperfinite geometric random walk) and the continuous model introduced by Black and Scholes (a geometric Brownian motion). Nonstandard methods provide a means of moving freely back and forth between the discrete and continuous points of view. This enables us to give an elementary derivation of the Black-Scholes option pricing formula from the corresponding formula for the binomial model. We also devise an intuitive but rigorous method for constructing self-financing hedge portfolios for various contingent claims, again using the explicit constructions available in the hyperfinite binomial model, to give the portfolio appropriate to the Black-Scholes model. Thus, nonstandard analysis provides a rigorous basis for the economists' intuitive notion that the Black-Scholes model contains a built-in version of the Cox-Ross-Rubinstein model.     

The Division of Labor Under Homogeneity: A Critique of Mises and Rothbard

A bstract .   Even the most passionate defenders of free trade, such as Mises and Rothbard, claim that trade cannot occur under conditions of strict homogeneity of land, labor, and capital. We show that specialization, trade, and the division of labor can emerge even when resources are initially homogenous, due to "natural heterogeneity," economies of scale, and learning.