Risk classification with on‐demand insurance

• Published date: 01 December 2023
• Author: Alexander Braun,Niklas Haeusle,Paul Thistle
• Date: 01 December 2023
• DOI: http://doi.org/10.1111/jori.12429

Received: 15 September 2020

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Revised: 19 April 2023

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Accepted: 22 April 2023

DOI: 10.1111/jori.12429

ORIGINAL ARTICLE

Risk classification with on‐demand insurance

Alexander Braun

1

|Niklas Haeusle

1

|Paul Thistle

2

1

Institute of Insurance Economics,

University of St. Gallen, St. Gallen,

Switzerland

2

Department of Finance, University

Nevada, Las Vegas, Nevada, USA

Correspondence

Alexander Braun and Niklas Haeusle,

Institute of Insurance Economics,

University of St. Gallen, IVW‐HSG, St.

Gallen, Switzerland.

Email: alexander.braun@unisg.ch and

niklas.haeusle@gmail.com

Abstract

On‐demand insurance is an innovative business

model from the InsurTech space, which provides

coverage for episodic risks. It makes use of a simple

fact in a practical way: People differ in their

frequency of exposure as well as the probability of

loss. The extra dimension of heterogeneity can

be used to screen the insured and shifts the

utility‐possibility frontier outward. We provide a

sufficient condition under which type‐specific full

insurance at the actuarially fair price is incentive

compatible. We also show that our results hold for

various real‐world implementations of on‐demand

insurance.

KEYWORDS

adverse selection, on‐demand insurance, risk classification,

screening

1|INTRODUCTION

On‐demand insurance is one of several innovations that the InsurTech sector has recently

brought to the insurance industry (Braun & Schreiber, 2017). It is quickly gaining relevance:

Some observers estimate that this nascent market could grow to $190 billion by 2026 (see,

e.g., Garth, 2019). The defining feature of on‐demand insurance is the coverage of episodic

risks. Consumers may use it for exclusive protection in periods during which they

themselves or their items are exposed. We distinguish two categories of on‐demand

Journal of Risk and Insurance. 2023;90:975–990. wileyonlinelibrary.com/journal/JORI

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This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and

reproduction in any medium, provided the original work is properly cited.

© 2023 The Authors. Journal of Risk and Insurance published by Wiley Periodicals LLC on behalf of American Risk and Insurance

Association.

insurance: (i) short‐term insurance and (ii) usage‐based insurance.

1

The first type is

designed to cover risks that are limited in duration or recurring and exhibit a known

exposure pattern over time (or at least one which is reliably predictable). Typical real‐world

manifestations are single‐trip travel insurance, interim accident insurance, temporary car

insurance, homeshare insurance,

2

and short‐term liability insurance for projects and

seasonal businesses. The second type, usage‐based insurance, in contrast, comes intoplay

when the time‐varying risk of consumers is stochastic. Representatives of this kind are pay‐

as‐you‐drive (pay‐per‐mile) or pay‐how‐you drive

3

car insurance, pay‐per‐use policies for

bicycles and cameras, gigworker liability coverage, and ridehailing coverage.

4

This paper analyzes on‐demand insurance contracts in markets with adverse selection. We

focus on the case in which exposure profiles over time are deterministic. Consumers may suffer

a loss of fixed size and belong to one of two risk types: a type with a high and a type with a low

total loss probability. In contrast to the classical one‐period setting, we account for the specific

characteristics of short‐term insurance by breaking down the loss state (main period) into

equidistant subperiods. Both insurers and consumers commit to price‐quantity contracts at the

beginning of the main period. Insurers are informationally constrained: the consumers' risk

types are private information. Total risk, subperiod risk, and prevalence of a given risk type, in

contrast, are public knowledge. The core contribution of our paper is twofold: First, starting

with the classical constrained maximization problem, we prove that introducing on‐demand

insurance contracts relaxes the incentive compatibility constraint of the high‐risk types and

thus expands the utility possibility frontier (UPF). Second, we derive a simple criterion under

which type‐specific actuarially fair full insurance is incentive compatible. We close our analysis

by showing that the same two basic results hold when we impose some additional

noninformational contract restrictions on the on‐demand insurance.

We contribute to the large literatures on risk classification (e.g., Crocker and Snow, 1985,

1986; Hoy, 1982; Rothschild, 2011,2015) and adverse selection (e.g., Eling et al., 2022; Hellwig,

1987; Rothschild & Stiglitz, 1976; Spence, 1978; Wilson, 1977) in insurance markets.

5

Our

problem exhibits similarities to the contributions of Bond and Crocker (1991), Finkelstein et al.

(2009), Crocker and Snow (2011), and Crocker and Zhu (2021).

6

Bond and Crocker (1991) allow insurance companies to classify risks based on the

observable consumption of goods, which is correlated with their privately known loss

propensity. They term this idea “endogenous categorization”and show that it may lead to first

best allocations, if the adverse selection problem is “small.”

7

Crocker and Zhu (2021) analyze

1

Zeier Röschmann et al. (2022) propose a similar definition for on‐demand insurance that also relies on the “coverage as‐needed”logic. Instead of

the stochasticity of the exposure profile, however, they differentiate the subforms accord ing to the mode of activation. In their definition, the

distinctive characteristic of usage‐based insurance is that coverage switches on automatically contin gent on location, activity, or context.

2

The risk profile of homeshare insurance is known if the owner makes his property available to rent at specific times of the year. Some

citizens of Munich, for example, rent out their apartment through AirBnB exclusively during Oktoberfest.

3

The pay‐how‐you‐drive concept takes usage‐based insurance beyond a single metric like miles. Rather, it encompasses telematics data,

taking into account acceleration and braking behavior, near‐miss events, and smartphone use while driving. This has implications for

motor insurance ratemaking and provides incentives for safe driving through weekly premium markups or discounts (Guillen

et al., 2021).

4

See the websites of Cuvva, Lings, and Slice for real‐world examples.

5

See Crocker and Snow (2013) and Dionne and Rothschild (2014) for comprehensive literature reviews. Similar to our study, Eling et al.

(2022) adopt the context of digital transformation. They consider the speed‐versus‐cost tradeoff arising from new technologies for

equilibria in insurance markets with adverse selection.

6

Our work is also related to the literature on contract form as a screening mechanism. This literature focuses on risk classification

through consumers' choices between mutual and stock insurance contracts (Ligon and Thistle, 2005; Smith and Stutzer, 1990), full and

limited tort coverage (Posey and Thistle, 2017) as well as regular and transparency contracts based on wearables or telematics devices

(Gemmo et al., 2017).

7

Bond and Crocker (1991) allow for both moral hazard and adverse selection, whereas we only consider an adverse selection problem.

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