Expected loss utility for natural hazards and its application in pricing property insurance products

Due to climatic hazards and extreme weather events, the pricing of property insurance products is increasingly attracting the attention of policyholders, insurance companies, and governments. Pricing based on market-oriented methods has to consider the affecting factors from policyholders’ perceived value. Pricing strategy design generates the need for natural hazards risk assessments. A natural hazard risk assessment is closely related to the human factors of a disaster-bearing body. In response to this need, we design an extension of the expected utility that is inconsistent with the additive expected utility, considering the human factors of policyholders, which is referred to as the expected loss utility (ELU). The ELU presents two improvements of the currently used utility. First, subjective probability, which is derived from individual predictions over acts, is applied to the ELU function to overcome the disadvantage that objective probability attaches to uncertainty does not reflect the uncertainty of human factors. Policyholders’ risk attitudes are reflected by the interpretation of interactions among uncertain events. Second, the hesitant fuzzy linguistic preference relation (HFLPR) is employed as the assessment of individual loss evaluation to reflect a policyholder’s hesitation. We apply the techniques of fuzzy linguistic term aggregation and perform a comparison to simplify our loss utility function. A detailed process of expected loss assessment is proposed due to variations in natural environment factors, local social characteristics, and disaster-bearing body factors. An illustrative example is given to perform a comparison with cumulative prospect theory to show the merits of the ELU. This study quantifies policyholder’s cognition of uncertain event and the cognition’s influence on risk assessment which can guide pricing strategy of property insurance products.