Can recipients of sales flyers be segmented?

This paper investigates the possibility of identifying clusters among consumers receiving sales flyers from retailers (supermarkets, etc.). First, flyers are defined and then consumers’ perception of flyers is analysed, based on a representative panel. According to the analysis, three clusters are identified. The clusters possess quite different characteristics – not just in relation to their perceptions and attitudes towards flyers, but also when looking at demographic characteristics.     

Neoclassical versus Frontier Production Models? Testing for the Skewness of Regression Residuals*

The empirical literature on production and cost functions is divided into two strands. The neoclassical approach concentrates on model parameters, while the frontier approach decomposes the disturbance term to a symmetric noise term and a positively skewed inefficiency term. We propose a theoretical justification for the skewness of the inefficiency term, arguing that this skewness is the key testable hypothesis of the frontier approach. We propose to test the regression residuals for skewness in order to distinguish the two competing approaches. Our test builds directly upon the asymmetry of regression residuals and does not require any prior distributional assumptions.     

Bankruptcy, Counterparty Risk, and Contagion

This paper provides a unifying framework for the modeling ofvarious types of credit risks such as contagion effects. Weargue that Markov chains can efficiently be used to tackle theseproblems. However, our approach is not limited to pricing problemswith contagion. On the theoretical side, we derive pricing formulasfor three building blocks that are generalizations of contingentclaims studied in Lando (1998). These claims can be thoughtof as atoms forming the basis for all credit risk payments.Furthermore, we demonstrate that, in general, all contingentclaims exposed to credit risk satisfy a system of partial differentialequations. This is the key result to calculate prices of creditrisk claims explicitly and efficiently.     

DISCRETE CHOICE AND RATIONAL INATTENTION: A GENERAL EQUIVALENCE RESULT

This article establishes a general equivalence between discrete choice and rational inattention models. Matějka and McKay (2015) showed that when information costs are modeled using the Shannon entropy, the choice probabilities in the rational inattention (RI) model take the multinomial logit form. We show that, for one given prior over states, RI choice probabilities may take the form of any additive random utility discrete choice model (ARUM) when the information cost is a Bregman information, a class defined in this article. The prior information of the rationally inattentive agent is summarized in a constant vector of utilities in the corresponding ARUM.     

Smooth investment

In the classical portfolio optimization problem considered by Merton, the resulting constant proportion investment plan requires a diffusive trading strategy. This means that, within any arbitrarily small time interval, the investor must impractically both buy and sell stocks. We study the problems of a mean-square and a power utility investor for whom the trading strategy is constrained to be smooth, i.e. nondiffusive. This means that over sufficiently small time intervals, the investor is either a seller or a buyer of stocks. The mathematical framework is built around quadratic objectives such that trading activity is punished quadratically. Mean-square utility is quadratic, and power utility is covered by quadratic punishment of distance to Merton’s power utility portfolio. We present semi-explicit solutions and, in a series of numerical illustrations, show the impact of trading constraints on the portfolio decision over the investment horizon.     

Stress scenario generation for solvency and risk management

We derive worst-case scenarios in a life insurance model in the case where the interest rate and the various transition intensities are mutually dependent. Examples of this dependence are that (a) surrender intensities and interest rates are high at the same time, (b) mortality intensities of a policyholder as active and disabled, respectively, are low at the same time, and (c) mortality intensities of the policyholders in a portfolio are low at the same time. The set from which the worst-case scenario is taken reflects the dependence structure and allows us to relate the worst-case scenario-based reserve, qualitatively, to a Value-at-Risk-based calculation of solvency capital requirements. This brings out perspectives for our results in relation to qualifying the standard formula of Solvency II or using a scenario-based approach in internal models. Our results are powerful for various applications and the techniques are non-standard in control theory, exactly because our worst-case scenario is deterministic and not adapted to the stochastic development of the portfolio. The formalistic results are exemplified in a series of numerical studies.     

Parisian types of ruin probabilities for a class of dependent risk-reserve processes

For a rather general class of risk-reserve processes, we provide an exact method for calculating different kinds of ruin probabilities, with particular emphasis on variations over Parisian type of ruin. The risk-reserve processes under consideration have, in general, dependent phase-type distributed claim sizes and inter-arrivals times, whereas the movement between claims can either be linear or follow a Brownian motion with linear drift. For such processes, we provide explicit formulae for classical, Parisian and cumulative Parisian types of ruin (for both finite and infinite time horizons) when the clocks are phase-type distributed. An erlangization scheme provides an efficient algorithmic methods for calculating the aforementioned ruin probabilities with deterministic clocks. Special attention is drawn to the construction of specific dependency structures, and we provide a number of numerical examples to study its effect on probabilities.     

The evolution of conventions under incomplete information

Summary. We formulate an evolutionary learning process with trembles for static games of incomplete information. For many games, if the amount of trembling is small, play will be in accordance with the games (strict) Bayesian equilibria most of the time. This supports the notion of Bayesian equilibrium. Often the process will select a specific equilibrium. We study an extension to incomplete information of the prototype conflict known as Chicken and find that the equilibrium selection by evolutionary learning may well be in favor of inefficient Bayesian equilibria where some types of players fail to coordinate.Received: 17 March 2003, Revised: 3 December 2003, JEL Classification Numbers: C72.