Multilinear Superhedging of Lookback Options

In a pathbreaking paper, Cover and Ordentlich (1998) solved a max-min portfolio game between a trader (who picks an entire trading algorithm, $\theta(\cdot)$) and "nature," who picks the matrix $X$ of gross-returns of all stocks in all periods. Their (zero-sum) game has the payoff kernel $W_\theta(X)/D(X)$, where $W_\theta(X)$ is the trader's final wealth and $D(X)$ is the final wealth that would have accrued to a $\$1$ deposit into the best constant-rebalanced portfolio (or fixed-fraction betting scheme) determined in hindsight. The resulting "universal portfolio" compounds its money at the same asymptotic rate as the best rebalancing rule in hindsight, thereby beating the market asymptotically under extremely general conditions. Smitten with this (1998) result, the present paper solves the most general tractable version of Cover and Ordentlich's (1998) max-min game. This obtains for performance benchmarks (read: derivatives) that are separately convex and homogeneous in each period's gross-return vector. For completely arbitrary (even non-measurable) performance benchmarks, we show how the axiom of choice can be used to "find" an exact maximin strategy for the trader.Comment: 41 pages, 3 figure

Software component testing : a standard and the effectiveness of techniques

This portfolio comprises two projects linked by the theme of software component testing, which is also often referred to as module or unit testing. One project covers its standardisation, while the other considers the analysis and evaluation of the application of selected testing techniques to an existing avionics system. The evaluation is based on empirical data obtained from fault reports relating to the avionics system. The standardisation project is based on the development of the BC BSI Software Component Testing Standard and the BCS/BSI Glossary of terms used in software testing, which are both included in the portfolio. The papers included for this project consider both those issues concerned with the adopted development process and the resolution of technical matters concerning the definition of the testing techniques and their associated measures. The test effectiveness project documents a retrospective analysis of an operational avionics system to determine the relative effectiveness of several software component testing techniques. The methodology differs from that used in other test effectiveness experiments in that it considers every possible set of inputs that are required to satisfy a testing technique rather than arbitrarily chosen values from within this set. The three papers present the experimental methodology used, intermediate results from a failure analysis of the studied system, and the test effectiveness results for ten testing techniques, definitions for which were taken from the BCS BSI Software Component Testing Standard. The creation of the two standards has filled a gap in both the national and international software testing standards arenas. Their production required an in-depth knowledge of software component testing techniques, the identification and use of a development process, and the negotiation of the standardisation process at a national level. The knowledge gained during this process has been disseminated by the author in the papers included as part of this portfolio. The investigation of test effectiveness has introduced a new methodology for determining the test effectiveness of software component testing techniques by means of a retrospective analysis and so provided a new set of data that can be added to the body of empirical data on software component testing effectiveness

Ambiguity and Social Interaction

We examine the impact of ambiguity on economic behaviour. We present a relatively non-technical account of ambiguity and show how it may be applied in economics. Optimistic and pessimistic responses to ambiguity are formally modelled. We show that pessimism has the effect of increasing (decreasing) equilibrium prices under Cournot (Bertrand) competition. We also examine the effects of ambiguity on peace processes. It is shown that ambiguity can act to select equilibria in coordination games with multiple equilibria. Some comparative statics results are derived for the impact of ambiguity in games with strategic complements.

Six causes of the credit crunch

Bank lending typically moves with the business cycle. In Texas from 1987 to 1992, however, bank loans declined while nonagricultural employment rose. Robert T. Clair and Paula Tucker consider this evidence of a constrained supply of bank loans, or credit crunch. ; Clair and Tucker find that multiple factors have reduced banks' willingness and ability to supply loans. The resolution of failed banks and thrifts, tightening of bank examination standards, new capital requirements, new regulations and increased enforcement of old regulations, and increased exposure to lawsuits have each had an effect. Many of these regulatory changes where made to address important economic and social goals, but their side effects, often unintended and perhaps unavoidable, have been to reduce bank lending in the short run.Credit