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

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- Working Paper (16)
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#### Keywords

- risk aversion (2)
- wealth inequality (2)
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- Asset-Backed Security (1)
- Bayes-Lernen (1)
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- Bedingungen der Anreizkompatibilität, Fundierung von Unternehmenszielen und Anreize für deren Umsetzung (2001)
- Vor dem Hintergrund allgemeiner Bedingungen der Anreizkompatibilität wird für verschiedenen Kapitalmarktmodelle untersucht, ob zwischen den Anteilseignern eines Unternehmens Einmütigkeit besteht und, wenn ja, mit welchem Unternehmensziel der finanzielle Nutzen der Anteilseigner maximiert wird. Von besonderer Bedeutung für die Anreizkompatibilität der üblichen linearen Erfolgsteilung ist die Bedingung pareto-effizienter Risikoteilung. Sind für den Erfolg des Unternehmens spezifische Störterme relevant und soll der Entscheidungsträger in relativ starkem Umfang am Erfolg beteiligt werden, ist die Risikoteilung zwischen ihm und den (anderen) Anteilseignern pareto-inferior. Anreizkompatible erfolgsorientierte Belohnungs- bzw. Prämienfunktionen für den Entscheidungsträger sind dann konvex und zustandsabhängig. Aktienoptionsprogramme können als Approximationen an solche Prämienfunktionen interpretiert werden.

- 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.

- 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.

- 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.

- Precautionary saving and the marginal propensity to consume out of permanent income (2009)
- The budget constraint requires that, eventually, consumption must adjust fully to any permanent shock to income. Intuition suggests that, knowing this, optimizing agents will fully adjust their spending immediately upon experiencing a permanent shock. However, this paper shows that if consumers are impatient and are subject to transitory as well as permanent shocks, the optimal marginal propensity to consume out of permanent shocks (the MPCP) is strictly less than 1, because buffer stock savers have a target wealth-to-permanent-income ratio; a positive shock to permanent income moves the ratio below its target, temporarily boosting saving. Keywords: Risk, Uncertainty, Consumption, Precautionary Saving, Buffer Stock Saving, Permanent Income Hypothesis.

- 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

- Are risk preferences dynamic? : Within-subject variation in risk-taking as a function of background music (2012)
- This paper investigates whether preference interactions can explain why risk preferences change over time and across contexts. We conduct an experiment in which subjects accept or reject gambles involving real money gains and losses. We introduce within-subject variation by alternating subjectively liked music and disliked music in the background. We find that favourite music increases risk-taking, and disliked music suppresses risk-taking, compared to a baseline of no music. Several theories in psychology propose mechanisms by which mood affects risktaking, but none of them fully explain our results. The results are, however, consistent with preference complementarities that extend to risk preference.

- 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.

- Saving rates and portfolio choice with subsistence consumption : [Version January 16, 2010] (2010)
- We analytically show that a common across rich/poor individuals Stone-Geary utility function with subsistence consumption in the context of a simple two-asset portfolio-choice model is capable of qualitatively explaining: (i) the higher saving rates of the rich, (ii) the higher fraction of personal wealth held in stocks by the rich, and (iii) the higher volatility of consumption of the wealthier. On the contrary, time-variant "keeping-up with the Joneses" weighted average consumption playing the role of moving benchmark subsistence consumption gives the same portfolio composition and saving rates across the rich and the poor, failing to reconcile the model with what micro data say.