Decision making with imprecise probabilities and its application

R. Lucas's Research Program: Far Too Narrow with Too Many Special Assumptions

In modern engineering, physical processes are modelled using advanced computer simulation tools (e.g. finite element models) to assess and optimize their performance. Moreover, awareness is growing on concepts like structural reliability and robust design, hence making the efficient quantification and propagation of uncertainties a key challenge. A major part of those analyses is the characterization of uncertainty in the input, which is typically done with probabilistic variables. In the case of sparse data sets, however, probability theory is often not the optimal choice. Imprecise probabilities provide a more general framework accounting for both aleatory and epistemic uncertainties. The uncertainty propagation of imprecise probabilities leads to imprecise responses. In this context, an algorithm for solving imprecise structural reliability problems is presented. The algorithm transforms the imprecise problem into two precise structural reliability problems, which opens up possibilities for using traditional structural reliability analyses techniques. An adaptive experimental design algorithm based on Polynomial-Chaos-Kriging is used to efficiently estimate imprecise failure probabilities. The capabilities of the framework are illustrated through an application using an analytical function and a realistic engineering problem setting.

An extension of chaotic probability models to real-valued variables

Behavioral decision making is an area of multidisciplinary research attracting growing interest of scientists and practitioners, economists, and business people. A wide spectrum of successful theories is present now, including Prospect theory, multiple priors models, studies on altruism, trust and fairness. However, these theories are developed for precise and complete information, whereas real information concerning a decision maker's (DM) behavior and environment is imperfect, qualitative, and, as a result, often described in natural language (NL). We suggest an approach based on modeling a DM's behavior by a set of states. Each state represents a certain principal behavior. In our approach, states of nature and DM's states constitute a single space of combined states. For formalizing relevant information described in NL, we use fuzzy set theory. The utility model is based on Choquet-like integration over combined states. The investigations show that Expected Utility, Choquet Expected Utility and Cumulative Prospect Theory are special cases of the suggested approach. We apply the suggested approach to solving a benchmark and a real-life decision problem. The obtained results show validity of the suggested approach.

An extension of the Becker proposition to non-expected utility theory

Most reliability models in the classical reliability theory use probability theory to quantify information under uncertainty and these models have a high demand of available data. While in practical applications, data related to system sand components are usually sparse or incomplete, moreover, some quantification of uncertainty should be based on subjective information and moreover subjective information may often be expressed in natural language. In these cases, classical reliability theory can not provide an effective way for the reliability analysis of systems. As a generalization of probability theory, imprecise probability theory may provide a tool which is called the natural extension to solve such problems. Research on the application of imprecise probability in reliability engineering has made a great progress. Unfortunately, this is all about theory and there are few applications and cases in practice. Therefore, this paper tried to overcome the flaws and shortcomings of classical reliability theory, and apply some theories of imprecise probability in practical engineering, and conduct reliability analysis on automotive semi-axle with establishing imprecise probability-based reliability model of automotive semi-axle. Natural extension is undoubtedly a powerful tool to compute reliability measures, however, when number of variables is large; the computation of natural extension is very difficult. Effective methods to simplify and build reliability models deserve more debate in the future.

Expected utility theory and inner and outer measures of loss aversion

Decision-making under uncertainty has evolved into a mature field. However, in most parts of the existing decision theory, one assumes decision makers have complete decision-relevant information. The standard framework is not capable to deal with partial or fuzzy information, whereas, in reality, decision-relevant information about outcomes, probabilities, preferences etc is inherently imprecise and as such described in natural language (NL). Nowadays, there is no decision theory with second-order uncertainty in existence albeit real-world uncertainties fall into this category. This applies, in particular, to imprecise probabilities expressed by terms such as likely, unlikely, probable, usually etc. We call such imprecise evaluations second-order information granules.

The first paper of this dissertation in Chapter II, “Insurance for Technology Adoption: An Experimental Evaluation of Schemes and Subsidies with Maize Farmers in Mexico”, analyzes experimentally how bundling the purchase of a risky technology, namely a higher yielding maize seed variety, with different insurance schemes, affects the total take-up of that variety. In this regard, the paper looks at the effects of (1) partial insurance versus full insurance, (2) geographical versus local basis risk, and (3) fair versus below-fair premium. This is the first paper to evaluate insurance schemes with different levels of risk reduction, basis risk and premium subsidies regarding their effect on technology adoption. The results add to the debate on insurance serving as a potential tool for incentivizing agricultural producers to adopt more productive, but more risky technologies, and thereby enabling them to escape poverty (Carter et al. 2016; Fan et al. 2013; Lybbert and Carter 2014; Nicola 2015; World Bank 2013). The second paper in Chapter III, “The Relationship between Farmers’ Shock Experiences and their Uncertainty Preferences - Experimental Evidence from Mexico” addresses the relationship between farmers’ uncertainty preferences, sociodemographic characteristics and their experience of adverse harvest shocks. Uncertainty preferences refer to a range of preference parameters as derived from Cumulative Prospect Theory (Kahneman and Tversky 1979; Tversky and Kahneman 1992), namely risk aversion, loss aversion and probability weighting, as well as ambiguity aversion (Ellsberg 1961). A series of incentivized lottery games are used to estimate these parameters with the sample of Mexican maize farmers, controlling for (1) sociodemographic characteristics and (2) the severity of experienced maize harvest losses. While there are several field studies examining the effect of shocks on risk preferences with subjects from developing countries, only few look at preferences beyond Expected Utility Theory and take into account Cumulative Prospect Theory, and none has looked at ambiguity aversion. Therefore, this paper sheds light on the role that the experience of adverse random shocks, as well as a range of sociodemographic variables, have in explaining one’s uncertainty preferences. The third paper in Chapter IV, “Formal Insurance, Risk Sharing, and the Dynamics of Other-Regarding Preferences”, analyzes how selectively providing formal insurance to members of a risk sharing network affects informal transfers and, subsequently, the dynamics of other-regarding preferences within that network. Many poor households in developing countries are excluded from formal financial markets and therefore rely on the mutual exchange within informal risk sharing networks to protect themselves against adverse income shocks. Social interactions in the aftermath of such shocks have been found to strengthen the social ties among members of these networks, while formal insurance has been found to crowd-out these transfers. Similarly, this third paper finds that when some members of risk sharing networks become formally insured, it affects the informal exchange of transfers among members, as well as their other-regarding preferences. This is the first study to explore the effect of insurance on other-regarding preferences in that context. In order to do so, an incentivized, three-stage experimental design with a baseline and an ex-post measurement of altruism, trust and trustworthiness through dictator and trust games is implemented with random and anonymous groups of three. Between the baseline and the ex-post measurement, a solidarity game is played with the same anonymous groups as in the ex-post measurement of other-regarding preferences, during which the shock structure and the availability of formal insurance are varied exogenously. The findings suggest that the effect of insurance depends on (1) the covariance structure of shocks and (2) is different for the insured and non-insured members within a network. Insurance either decreases trust levels of the uninsured or increases trust levels of the insured subjects towards the other network members, depending on whether the shocks affects one or more than one network member at a time. Trustworthiness and altruism remain unaffected by insurance. Furthermore, the analysis indicates that the results are driven by a change in the dynamics of the transfer behavior within the network induced by formal insurance. Specifically, there is evidence that subjects increase trust levels towards their network members after receiving higher transfers relative to the maximum possible value from them, but not after receiving higher transfers in absolute terms.

In this paper, we construct new valuation schemes for the liabilities and economic capital of insurance companies. Specifically, we first build a ‘SAHARA’ valuation framework based on Symmetric Asymptotic Hyperbolic Absolute Risk Aversion utility functions. Then, we construct a ‘SAHARA-CPT’ framework that incorporates the previous utility function as a value function and that is based on Cumulative Prospect Theory. The process used for assessing a life insurance company’s own funds consists in replacing the market-consistent parametrization with a utility-consistent parametrization that accounts for the risk aversion of the market and the long-term duration of the company’s commitments. Our illustrations show that this approach leads to a lower value of the Own Risk and Solvency Assessment and to a lower volatility of own funds. The framework that is based on cumulative prospect theory has the advantage over the expected utility theory framework that it considers a precautionary overweighting of extreme events, as a tradeoff for additional model complexity.

Perception du risque routier par les adultes rhodaniens – département du Rhône, France

Toward a perception-based theory of probabilistic reasoning with imprecise probabilities

Nonlinear decision weights or moment-based preferences? A model competition involving described and experienced skewness

Probabilistically distorted risk-sensitive infinite-horizon dynamic programming

Geometric Dispersion Theory for Decisions Under Risk: Accurate Out-of-Sample Predictions and Four Distinct Behavioral Patterns