Hidden insurance in a moral‐hazard economy

Abstract

We consider an economy where individuals privately choose effort and trade competitively priced securities that pay off with effort-determined probability. We show that if insurance against a negative shock is sufficiently incomplete, then standard functional form restrictions ensure that individual objective functions are optimized by an effort and insurance combination that is unique and satisfies first-and second-order conditions. Modeling insurance incompleteness in terms of costly production of private insurance services, we characterize the constrained inefficiency arising in general equilibrium from competitive pricing of nonexclusive financial contracts.

On the validity of the first-order approach with moral hazard and hidden assets

“…Bertola and Koeniger (2013) provide similarly plausible and appealing conditions for an economy with hidden insurance against a single contingency, as in Pauly (1974). In an even mildly more complex and realistic economy, where both non-contingent savings and insurance against a single contingent event are hidden, such restrictions do not suffice to prove validity of the first-order approach building on the approach of Rogerson (1985).…”

“…As in Ábrahám, Koehne and Pavoni (2011) and Bertola and Koeniger (2013), a promising restriction for the distribution function is…”

“…In models with a single hidden asset, it is possible to formulate functional form conditions that, together with , where > 0 is the size of a single negative shock covered by non-exclusive insurance, Bertola and Koeniger (2013) show that the concavity of u (c(z 2 )) is dominated by convexity of u (c(z 1 )) if absolute risk aversion is decreasing and insurance is sufficiently incomplete, i.e., the asset quantity is in (0; ). The latter condition is satisfied at the optimum if insurance is actuarially unfair enough and implies large enough differences in consumption c(z 2 ) and c(z 1 ), and thus also in utility.…”

“…In that setting, Bertola and Koeniger (2013) derive functional form restrictions ensuring validity of that "first-order approach. " Ábrahám, Koehne and Pavoni (2011) similarly establish that first-order conditions are necessary and sufficient, under sensible and interpretable functional restrictions, in an economy with exclusive formal insurance and a single hidden non-contingent asset.…”

Evaluating the Creditworthiness of the Client in Insurance Industry Using Adaptive Neuro-Fuzzy Inference System

“…The insurance industry (Biener, Eling & Wirfs, 2016), as one of the segments of national economy, currently ranks among significant sectors and represents an indispensable part of the modern society (Ma, 2015). By its nature, it is involved in all economic activities (Bertola & Koeniger, 2015), affects market economy and mediates the creation of new job opportunities (Kwon, 2014). It provides one of the possible responses to risk both to businesses and individuals (Xuan, Meng & Dongli, 2010).…”