Nash equilibrium strategies in discrete-time finite-horizon dynamic games with risk-and effort-averse players

The objective of this paper is to re-examine the risk-and effort attitude in the context of strategic dynamic interactions stated as a discrete-time finite-horizon Nash game. The analysis is based on the assumption that players are endogenously risk-and effort-averse. Each player is characterized by distinct risk-and effort-aversion types that are unknown to his opponent. The goal of the game is the optimal risk-and effort-sharing between the players. It generally depends on the individual strategies adopted and, implicitly, on the the players' types or characteristics.

Stochastic dominance and absolute risk aversion

In this paper we propose the infimum of the Arrow-Pratt index of absolute risk aversion as a measure of global risk aversion of a utility function. We then show that, for any given arbitrary pair of distributions, there exists a threshold level of global risk aversion such that all increasing concave utility functions with at least as much global risk aversion would rank the two distributions in the same way. Furthermore, this threshold level is sharp in the sense that, for any lower level of global risk aversion, we can find two utility functions in this class yielding opposite preference relations for the two distributions.

Subjective income expectations, canonical models and income risk

Expectations are central to behaviour. Despite the existence of subjective expectations data, the standard approach is to ignore these, to hypothecate a model of behaviour and to infer expectations from realisations. In the context of income models, we reveal the informational gain obtained from using both a canonical model and subjective expectations data. We propose a test for this informational gain, and illustrate our approach with an application to the problem of measuring income risk.

Investor protection, risk sharing and inequality

This paper studies the relationship between investor protection, financial risk sharing and income inequality. In the presence of market frictions, better protection makes investors more willing to take on entrepreneurial risk while lending to firms. This implies lower cost of external finance and better risk sharing between financiers and entrepreneurs. Investor protection, by boosting the market for risk sharing plays the twofold role of encouraging agents to undertake risky enterprises and providing them with insurance. By increasing the number of risky projects, it raises income inequality. By extending insurance to more agents, it reduces it. As a result, the relationship between the size of the market for risk sharing and income inequality is hump-shaped. Empirical evidence from a cross-section of sixty-eight countries, and a panel of fifty countries over the period 1976-2000, supports the predictions of the model.

Improving the risk concept: a revision of Arrow-Pratt theory in the context of controlled dynamic stochastic environments

In the literature on risk, one generally assume that uncertainty is uniformly distributed over the entire working horizon, when the absolute risk-aversion index is negative and constant. From this perspective, the risk is totally exogenous, and thus independent of endogenous risks. The classic procedure is "myopic" with regard to potential changes in the future behavior of the agent due to inherent random fluctuations of the system. The agent's attitude to risk is rigid. Although often criticized, the most widely used hypothesis for the analysis of economic behavior is risk-neutrality. This borderline case must be envisaged with prudence in a dynamic stochastic context. The traditional measures of risk-aversion are generally too weak for making comparisons between risky situations, given the dynamic �complexity of the environment. This can be highlighted in concrete problems in finance and insurance, context for which the Arrow-Pratt measures (in the small) give ambiguous.

Optimal feedback control rules sensitive to controlled endogenous risk-aversion

The objective of this paper is to correct and improve the results obtained by Van der Ploeg (1984a, 1984b) and utilized in the theoretical literature related to feedback stochastic optimal control sensitive to constant exogenous risk-aversion (see, Jacobson, 1973, Karp, 1987 and Whittle, 1981, 1989, 1990, among others) or to the classic context of risk-neutral decision-makers (see, Chow, 1973, 1976a, 1976b, 1977, 1978, 1981, 1993). More realistic and attractive, this new approach is placed in the context of a time-varying endogenous risk-aversion which is under the control of the decision-maker. It has strong qualitative implications on the agent's optimal policy during the entire planning horizon.

Risk Attitude And Wage Growth: Replication And Reconstruction

We replicate Shaw (1996) who found that individual wage growth is higher for individuals with greater preference for risk taking. Expanding her dataset with more American observations and data for Germany, Spain and Italy, we find mixed support for the earlier results. We present and estimate a new model and find that in particular the wage level is sensitive to attitudes towards risk taking. Comments given at the Labour Economics Conference in honour of Niels Westergaard (Nyborg, August 2008) and EALE 2008 (Amsterdam) and at seminars in Maastricht,Reus and Essen (RWI) are gratefully acknowledged. The authors also acknowledge financial support from the Spanish Ministry of Science and Innovation (grant number SEJ2007-66318) and from the Barcelona Economics Program of CREA. JEL code: J24; J30. Key words: wage growth, risk, post-school investment.

Dynamic stackelberg game with risk-averse players: optimal risk-sharing under asymmetric information

The objective of this paper is to clarify the interactive nature of the leader-follower relationship when both players are endogenously risk-averse. The analysis is placed in the context of a dynamic closed-loop Stackelberg game with private information. The case of a risk-neutral leader, very often discussed in the literature, is only a borderline possibility in the present study. Each player in the game is characterized by a risk-averse type which is unknown to his opponent. The goal of the leader is to implement an optimal incentive compatible risk-sharing contract. The proposed approach provides a qualitative analysis of adaptive risk behavior profiles for asymmetrically informed players in the context of dynamic strategic interactions modelled as incentive Stackelberg games.

Preference intensities and risk aversion in school choice: a laboratory experiment

We experimentally investigate in the laboratory two prominent mechanisms that are employed in school choice programs to assign students to public schools. We study how individual behavior is influenced by preference intensities and risk aversion. Our main results show that (a) the Gale-Shapley mechanism is more robust to changes in cardinal preferences than the Boston mechanism independently of whether individuals can submit a complete or only a restricted ranking of the schools and (b) subjects with a higher degree of risk aversion are more likely to play "safer" strategies under the Gale-Shapley but not under the Boston mechanism. Both results have important implications for the efficiency and the stability of the mechanisms.

Investor protection and income inequality: risk sharing vs risk taking

This paper studies the relationship between investor protection, entrepreneurial risk taking and income inequality. In the presence of market frictions, better protection makes investors more willing to take on entrepreneurial risk when lending to firms, thereby improving the degree of risk sharing between financiers and entrepreneurs. On the other hand, by increasing risk sharing, investor protection also induces more firms to undertake risky projects. By increasing entrepreneurial risk taking, it raises income dispersion. By reducing the risk faced by entrepreneurs, it reduces income volatility. As a result, investor protection raises income inequality to the extent that it fosters risk taking, while it reduces it for a given level of risk taking. Empirical evidence from a panel of forty-five countries spanning the period 1976-2000 supports the predictions of the model.

Work, risk and health: differences between immigrants and natives in Spain

We analyze the impact of working and contractual conditions, particularly exposure to job risks, on the probability of acquiring a disability. We postulate a model in which this impact is mediated by the choice of occupation, with a level of risk associated to it. We assume this choice is endogenous, and that it depends on preferences and opportunities in the labour market, both of which may differ between immigrants and natives. To test this hypothesis we use data from the Continuous Sample of Working Lives of the Spanish SS system. It contains individual, job and firm information of over a million workers, including a representative sample of immigrants. We find that risk exposure increases the probability of permanent disability by 5.3%; temporary employment also influences health. Migrant status -with differences among regions of origin- significantly affects both disability and the probability of being employed in a risky occupation. Most groups of immigrants work in riskier jobs, but have lower probability of becoming disabled. Nevertheless, our theoretical hypothesis that disability and risk are jointly determined is not valid for immigrants: i.e. for them working conditions is not a matter of choice in terms of health.

How much risk is mitigated by LTC Insurance? A case study of the public system in Spain

We present a methodology that allows to calculate the impact of a given Long-Term Care (LTC) insurance protection system on the risk of incurring extremely large individual lifetime costs. Our proposed methodology is illustrated with a case study. According to our risk measure, the current Spanish public LTC system mitigates individual risk by more than 30% compared to the situation where no public protection were available. We show that our method can be used to compare risk reduction of alternative LTC insurance plans.

Loss risk through fraud in car insurance

Our objective is to analyse fraud as an operational risk for the insurance company. We study the effect of a fraud detection policy on the insurer's results account, quantifying the loss risk from the perspective of claims auditing. From the point of view of operational risk, the study aims to analyse the effect of failing to detect fraudulent claims after investigation. We have chosen VAR as the risk measure with a non-parametric estimation of the loss risk involved in the detection or non-detection of fraudulent claims. The most relevant conclusion is that auditing claims reduces loss risk in the insurance company.