## D81 Criteria for Decision-Making under Risk and Uncertainty

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- risk aversion (2)
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- Asset pricing under rational learning about rare disasters : [Version 28 Juli 2011] (2011)
- This paper proposes a new approach for modeling investor fear after rare disasters. The key element is to take into account that investors’ information about fundamentals driving rare downward jumps in the dividend process is not perfect. Bayesian learning implies that beliefs about the likelihood of rare disasters drop to a much more pessimistic level once a disaster has occurred. Such a shift in beliefs can trigger massive declines in price-dividend ratios. Pessimistic beliefs persist for some time. Thus, belief dynamics are a source of apparent excess volatility relative to a rational expectations benchmark. Due to the low frequency of disasters, even an infinitely-lived investor will remain uncertain about the exact probability. Our analysis is conducted in continuous time and offers closed-form solutions for asset prices. We distinguish between rational and adaptive Bayesian learning. Rational learners account for the possibility of future changes in beliefs in determining their demand for risky assets, while adaptive learners take beliefs as given. Thus, risky assets tend to be lower-valued and price-dividend ratios vary less under adaptive versus rational learning for identical priors. Keywords: beliefs, Bayesian learning, controlled diffusions and jump processes, learning about jumps, adaptive learning, rational learning. JEL classification: D83, G11, C11, D91, E21, D81, C61

- Representing consumption and saving without a representative consumer (2014)
- The Great Recession confirmed a bedrock principle of modern consumption theory: It is impossible to explain aggregate spending behavior without knowledge of the underlying microeconomic distribution of circumstances and choices across households. National accounting frameworks therefore need to be augmented by “bottom up” measures that both (a) capture the microeconomic heterogeneity (in expenditures, income, assets, debt, and beliefs) in the population and (b) sum up to statistics that have a recognizable relationship to the aggregate totals that are already reasonably well measured.

- Collateralised loan obligations (CLOs) : a primer (2002)
- The following descriptive paper surveys the various types of loan securitisation and provides a working definition of so-called collateralised loan obligations (CLOs). Free of the common rhetoric and slogans, which sometimes substitute for understanding of the complex nature of structured finance, this paper describes the theoretical foundations of this specialised form of loan securitisation. Not only the distinctive properties of CLOs, but also the information economics inherent in the transfer of credit risk will be considered, so that we can equally privilege the critical aspects of security design in the structuring of CLO transactions.

- Catastrophe index-linked securities and reinsurance as substituties (2000)
- The use of catastrophe bonds (cat bonds) implies the problem of the so called basis risk, resulting from the fact that, in contrast to traditional reinsurance, this kind of coverage cannot be a perfect hedge for the primary’s insured portfolio. On the other hand cat bonds offer some very attractive economic features: Besides their usefulness as a solution to the problems of moral hazard and default risk, an important advantage of cat bonds can be seen in the presumably lower transaction costs compared to (re)insurance products. Insurance coverage usually incurs costs of acquisition, monitoring and loss adjustment, all of which can be reduced by making use of the financial markets. Additionally, cat bonds are only weakly correlated with market risk, implying that in perfect financial markets these securities could be traded at a price including just small risk premiums. Although these aspects have been identified in economic literature, to our knowledge there has been no publication so far that formally addresses the trade-off between basis risk and transaction cost. In this paper, therefore, we introduce a simple model that enables us to analyze cat bonds and reinsurance as substitutional risk management tools in a standard insurance demand theory environment. We concentrate on the problem of basis risk versus transaction cost, and show that the availability of cat bonds affects the structure of optimal reinsurance contract design in an interesting way, as it leads to an increase of indemnity for small losses and a decrease of indemnity for large losses.

- Hidden insurance in a moral hazard economy (2013)
- We consider an economy where individuals privately choose effort and trade competitively priced securities that pay off with effort-determined probability. We show that if insurance against a negative shock is sufficiently incomplete, then standard functional form restrictions ensure that individual objective functions are optimized by an effort and insurance combination that is unique and satisfies first- and second-order conditions. Modeling insurance incompleteness in terms of costly production of private insurance services, we characterize the constrained inefficiency arising in general equilibrium from competitive pricing of nonexclusive financial contracts.

- Hidden regret in insurance markets : adverse and advantageous selection (2008)
- We examine insurance markets with two types of customers: those who regret suboptimal decisions and those who don.t. In this setting, we characterize the equilibria under hidden information about the type of customers and hidden action. We show that both pooling and separating equilibria can exist. Furthermore, there exist separating equilibria that predict a positive correlation between the amount of insurance coverage and risk type, as in the standard economic models of adverse selection, but there also exist separating equilibria that predict a negative correlation between the amount of insurance coverage and risk type, i.e. advantageous selection. Since optimal choice of regretful customers depends on foregone alternatives, any equilibrium includes a contract which is o¤ered but not purchased.

- On the relation between robust and Bayesian decision making (2003)
- This paper compares Bayesian decision theory with robust decision theory where the decision maker optimizes with respect to the worst state realization. For a class of robust decision problems there exists a sequence of Bayesian decision problems whose solution converges towards the robust solution. It is shown that the limiting Bayesian problem displays infinite risk aversion and that decisions are insensitive (robust) to the precise assignment of prior probabilities. This holds independent from whether the preference for robustness is global or restricted to local perturbations around some reference model.

- Measuring ambiguity aversion: a systematic experimental approach : [Version 20 June 2014] (2014)
- This paper provides a systematic analysis of individual attitudes towards ambiguity, based on laboratory experiments. The design of the analysis allows to capture individual behavior across various levels of ambiguity, ranging from low to high. Attitudes towards risk and attitudes towards ambiguity are disentangled, providing pure measures of ambiguity aversion. Ambiguity aversion is captured in several ways, i.e. as a discount factor net of a risk premium, and as an estimated parameter in a generalized utility function. We find that ambiguity aversion varies across individuals, and with the level of ambiguity, being most prominent for intermediate levels. Around one third of subjects show no aversion, one third show maximum aversion, and one third show intermediate levels of ambiguity aversion, while there is almost no ambiguity seeking. While most theoretical work on ambiguity builds on maxmin expected utility, our results provide evidence that MEU does not adequately capture individual attitudes towards ambiguity for the majority of individuals. Instead, our results support models that allow for intermediate levels of ambiguity aversion. Moreover, we find risk aversion to be statistically unrelated to ambiguity aversion on average. Taken together, the results support the view that ambiguity is an important and distinct argument in decision making under uncertainty.

- Stochastic differential utility as the continuous-time limit of recursive utility (2013)
- We establish a convergence theorem that shows that discrete-time recursive utility, as developed by Kreps and Porteus (1978), converges to stochastic differential utility, as introduced by Dufffie and Epstein (1992), in the continuous-time limit of vanishing grid size.