Bridging the gap between risk and uncertainty in insurance

This contribution evokes Orio Giarini’s courage to think ‘outside the box’. It proposes a practical way to bridge the gap between risk (where probabilities of occurrence are fully known) and uncertainty (where these probabilities are unknown). However, in the context of insurance, neither extreme applies: the risk type of a newly enrolled customer is not fully known, loss distributions (especially their tails) are difficult to estimate with sufficient precision, the diversification properties of a block of policies acquired from another company can be assessed only to an approximation, and rates of return on investment depend on decisions of central banks that cannot be predicted too well. This contribution revolves around the launch of an innovative insurance product, where the company has a notion of whether a favourable market reception is more likely than an unfavourable one, of the chance of obtaining approval from the regulatory authority and the risk of a competitor launching a similar innovation. Linear partial information theory is proposed and applied as a particular practical way to systematically exploit the imprecise information that may exist for all of these aspects. The decision-making criterion is maxEmin, an intuitive modification of the maximin rule known from games against nature.

An inexact multi-stage interval-parameter partial information programming model for water resources management under uncertainties

The urban water shortage crisis around the world is increasing. In this study, an inexact multi-stage interval-parameter partial information programming model (IMIPM) is proposed for urban water resources planning and management under uncertainties. Optimization techniques of two-stage stochastic programming (TSP), interval-parameter programming (IPP), linear partial information theory (LPI) and multistage stochastic programming (MSP) are combined into one general framework. IMIPM is used to tackle uncertainties like interval numbers, water inflow probabilities expressed as linear partial information, dynamic features in a long planning time and joint probabilities in water resources management. It is applied to Harbin where the manager needs to allocate water from multi-water sources to multi-water users during multi-planning time periods. Four water flow probability scenarios are obtained, which are associated with uncertainties of urban rainfall information. The results show that the dynamics features and uncertainties of system parameters (such as water allocation targets and shortage) are considered in this model by generating a set of representative scenarios within a multistage context. The results also imply that IMIPM can truly reflect the actual urban water resources management situation, and provide managers with decision-making space and technical support to promote the sustainable development of economics and the ecological environment in cities.

Determining statistical dominance by linear programming

This note generalises the necessary and sufficient conditions for one act to be dominated by another when the two acts available to the decision maker have outcomes contingent on discrete states of nature whose probabilities of occurrence are known only to the extent of linear partial information. The generalisation relates to the dominance of an act by a set of acts. The presentation is in terms of general vector dominance, of which statistical dominance is only a particular case.