Purpose – To: evaluate Prospect Theory and Cumulative Prospect Theory as functional models of decision making and risk within various contexts; compare and analyze risk models and decision-making models; evaluate models of stock risk developed by Robert Engle and related models; establish whether the models are related and have the same foundations; relate risk, decision making and options theory; and develop the foundations for a new model of decision making and risk named “belief systems”. Design/methodology/approach – Critiques existing academic work in different contexts. Analyzes the shortcomings of various measures of risk, and group decision making, which was not addressed in developing Prospect Theory and Cumulative Prospect Theory. Develops the characteristics of a mew model for decision making and risk named “belief systems”, and then differentiates it from belief networks. Findings – Decision making is a multi-factor, multi-dimensional process that often requires the processing of information, and thus, it is inaccurate to impose rigid models in decision making; the existing metrics for quantifying risk are inadequate; Prospect Theory and Cumulative Prospect Theory were developed using questionable methods and data, and are impractical; the analysis of probabilistic insurance and most of the theories and “effects” developed by Kahneman and Tversky's articles are invalid and impractical; Prospect Theory, Cumulative Prospect Theory, Expected Utility Theory, and market-risk models are conceptually the same and do not account for many facets of risk and decision making; risk and decision making are better quantified and modeled using a mix of situation-specific dynamic, quantitative and qualitative factors; belief systems can better account for the multi-dimensional characteristics of risk and decision making. Research limitations/implications – Areas for further research include: development of dynamic market-risk models that incorporate asset-market psychology, liquidity, market size, frequency of trading, knowledge differences among market participants, and trading rules in each market; and further development of concepts in belief systems. Practical implications – Decision making and risk assessment are multi-criteria processes that typically require some processing of information, and thus cannot be defined accurately by rigid quantitative models; Prospect Theory and Cumulative Prospect Theory are abstract, rigid, and are not practical models for decision making; and existing market-risk models are inaccurate, and thus the international financial system may be compromised. Originality/value – The issues discussed are relevant to government regulators, central banks, judges, risk managers, executives, derivatives regulators, stock exchange regulators, legislators, psychologists, boards of directors, finance professionals, management science/operations research professionals, health-care-informatics professionals, scientists, engineers, and people in any situation that requires decision making and risk assessment.