Terje Lensberg

Genetic programming and rough sets: A hybrid approach to bankruptcy classification

Abstract The high social costs associated with bankruptcy have spurred searches for better theoretical understanding and prediction capability. In this paper, we investigate a hybrid approach to bankruptcy prediction, using a genetic programming algorithm to construct a bankruptcy prediction model with variables from a rough sets model derived in prior research. Both studies used data from 291 US public companies for the period 1991 to 1997. The second stage genetic programming model developed in this research consists of a decision model that is 80% accurate on a validation sample as compared to the original rough sets model which was 67% accurate. Additionally, the genetic programming model reveals relationships between variables that are not apparent in either the rough sets model or prior research. These findings indicate that genetic programming coupled with rough sets theory can be an efficient and effective hybrid modeling approach both for developing a robust bankruptcy prediction model and for offering additional theoretical insights.

Bankruptcy theory development and classification via genetic programming

Abstract Bankruptcy is a highly significant worldwide problem with high social costs. Traditional bankruptcy risk models have been criticized for falling short with respect to bankruptcy theory building due to either modeling assumptions or model complexity. Genetic programming minimizes the amount of a priori structure that is associated with traditional functional forms and statistical selection procedures, but still produces easily understandable and implementable models. Genetic programming was used to analyze 28 potential bankruptcy variables found to be significant in multiple prior research studies, including 10 fraud risk factors. Data was taken from a sample of 422 bankrupt and non-bankrupt Norwegian companies for the period 1993–1998. Six variables were determined to be significant. A genetic programming model was developed for the six variables from an expanded sample of 1136 bankrupt and non-bankrupt Norwegian companies. The model was 81% accurate on a validation sample, slightly better than prior genetic programming research on US public companies, and statistically significantly better than the 77% accuracy of a traditional logit model developed using the same variables and data. The most significant variable in the final model was the prior auditor opinion, thus validating the information value of the auditor’s report. The model provides insight into the complex interaction of bankruptcy related factors, especially the effect of company size. The results suggest that accounting information, including the auditor’s evaluation of it, is more important for larger than smaller firms. It also suggests that for small firms the most important information is liquidity and non-accounting information. The genetic programming model relationships developed in this study also support prior bankruptcy research, including the finding that company size decreases bankruptcy risk when profits are positive. It also confirms that very high profit levels are associated with increased bankruptcy risk even for large companies an association that may be reflecting the potential for management to be “Cooking the Books”.

Stability and the Nash solution

Abstract In an axiomatic bargaining model with a variable number of agents, a stability axiom due to Harsanyi is used to give a characterization of the Nash bargaining solution without independence of irrelevant alternatives. Our main result is that the Nash solution is the only one to satisfy Pareto optimality, anonymity, scale invariance, and stability. We also show that the stability axiom allows one to weaken Pareto optimality to what we call individual optimality and still permit a characterization of the Nash solution.

STABILITY AND COLLECTIVE RATIONALITY

A collective choice problem involves a set of agents and a set of feasi ble utility vectors. Many solutions to the collective choice problem (e.g., the Nash solution) are collectively rational, i.e., consistent with the maximization of some ordering of utility space. In this pap er, a stability condition due to J. C. Harsanyi is used to obtain the following integrability result: any solution satisfying Pareto optim ality, continuity, and bilateral stability can be represented by an a dditively separable Bergson-Samuelson social welfare function. Copyright 1987 by The Econometric Society.

Characterizing the Nash bargaining solution without Pareto-Optimality

We consider the bargaining problems with a variable number of agents. Lensberg had previously characterized the Nash solution as the only solution to satisfy the following axioms: Pareto-Optimality, Symmetry, Scale Invariance, and Multilateral Stability. We show that the disagreement solution is the only additional solution to satisfy the restricted list of axioms obtained by dropping Pareto-Optimality.

Guarantee structures for problems of fair division

Abstract We study the problem of fair division in situations where the number of individuals involved may vary while the resources at their disposal remain fixed. We are interested in minimizing the loss that an agent originally present may incur in such circumstances. Given a solution , i.e., a systematic method of solving any division problem in some class, we introduce the notion of its guarantee structure as a measure of the protection it offers to the original agents. We show that the Kalai-Smorodinsky solution offers greater guarantees than any weakly Pareto-optimal and anonymous solution and in particular than the Nash solution.

A Note on the Cost of Collecting Wealth Taxes

We use a CAPM model to estimate the cost of collecting wealth taxes from private Norwegian owners. The cost consists of foregone investment opportunities due to higher required returns on equity. For listed firms, the cost is zero. For non-listed firms, it amounts to more than 250% of the tax revenue.

Hedging without Sweat: A Genetic Programming Approach

Hedging in the presence of transaction costs leads to complex optimization problems. These problems typically lack closed-form solutions, and their implementation relies on numerical methods that provide hedging strategies for specific parameter values. In this paper, we use a genetic programming algorithm to derive explicit formulas for near-optimal hedging strategies under nonlinear transaction costs. The strategies are valid over a large range of parameter values and require no information about the structure of the optimal hedging strategy.

Axiomatic Theory of Bargaining with a Variable Number of Agents: Axiomatic theory of bargaining with a fixed number of agents

In this book, Professor Thomson and Professor Lensberg extrapolate upon the Nash (1950) treatment of the bargaining problem to consider the situation where the number of bargainers may vary. The authors formulate axioms to specify how solutions should respond to such changes, and provide new characterizations of all the major solutions as well as generalizations of these solutions. The book also contains several other comparative studies of solutions in the context of a variable number of agents. Much of the theory of bargaining can be rewritten within this context. The pre-eminence of the three solutions at the core of the classical theory is confirmed. These are the solutions introducted by Nash (1950) and two solutions axiomatized in the 1970s (Kalai-Smorodinsky and egalitarian solutions).

Front-Running and Market Quality: An Evolutionary Perspective on High Frequency Trading†

We study front-running by high-frequency traders (HFTs) in a limit order model with continuous trading. The model describes an evolutionary equilibrium of low-frequency traders who compete in portfolio management services by offering investment styles. The introduction of front-runners inflicts heavy losses on speculators, while leaving passive investors relatively unscathed. This encourages investment in the market portfolio and markedly reduces overall turnover. Speculative trading persists despite its lower profitability. By most measures, market quality is not affected to any significant extent by front-running HFTs.