The broker model for peer-to-peer insurance: an analysis of its value

Abstract

The increasing role of technology is generating new challenges in fostering innovative insurance products and in offering new means of distribution for existing products. Herein, we focus on peer-to-peer insurance, where technology is used to connect policyholders and the insurance structure recalls its roots based on organised mutual solidarity. The aim is to highlight strengths and weaknesses of the broker model of peer-to-peer insurance. We address the main legal and regulatory issues by referring to European Union regulation on insurance and we develop an actuarial model to support our conclusions and evaluate the convenience of such a business model for policyholders. Although peer-to-peer insurance was created as a fairer alternative to the pool of traditional insurance companies, we see major challenges that need to be solved. The evidence sheds doubt on the convenience of the broker model for peer-to-peer insurance while the regulatory risks seem, paradoxically, certain.

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Notes

  1. 1.

    The pioneer in the development of this model of insurance was Friendsurance (D) in 2010, followed by Guevara (U.K.) and Inspeer (FR). TongJuBao (CN) and Lemonade (U.S.) followed.

  2. 2.

    This definition was later reproduced by IAIS (2017), p. 40.

  3. 3.

    The Institute of International Finance (IIF 2016) p.11, outlines that “Unlike P2PI brokers, P2PI carriers do the actual underwriting and offer their policies directly to consumers online. The business model allows investors to participate in the process and contribute money toward the capital reserves for the various insurance pools. Once the required period of time has elapsed, and after all claims have been paid, the investors and the carrier firm divide the outstanding balance remaining in the premium pool.”.

  4. 4.

    Teambrella uses this model (Paperno et al. 2016).

  5. 5.

    EIOPA (2019), p. 29 reported that such a technical service provider might leverage Blockchain and smart contracts and facilitate users coming together and creating their own “pools”.

  6. 6.

    For instance, FriendInsurance, Inspeer, PeerCover, Guevara and Axieme follow this model.

  7. 7.

    The IIF outlined that most P2P insurance schemes act as brokers and aim to lower the cost of insurance for their consumers by pooling policyholders together online and leveraging their buying power. (IIF 2016).

  8. 8.

    EIOPA (2019), p.26 outlined that it is a matter of evaluating concrete business models and the outcome can be that a platform is operating under insurance regulation, or that it is outside of regulation, e.g. in the context of payments services.

  9. 9.

    Lima Rego and Campos Carvalho (2019) reached the conclusion that, to a large extent, the leading characters in P2P insurance appear to play the same roles traditionally ascribed to insurers and insurance intermediaries in ordinary B2C contexts.

  10. 10.

    From the FriendInsurance.de website: “Wir verbinden Sie mit anderen Versicherten zu einer Gruppe von durchschnittlich 10 Personen. Die Gruppe macht Ihren Bonus überhaupt erst möglich. Ohne Gruppe geht es nicht”, i.e., we connect you with other insured persons to a group of on average 10 persons. The group makes your bonus possible in the first place. It cannot be done without a group. Axieme connects people to other people with the same rating that bought the same contracts. Lemonade places people that select the same charity for the cashback in the same group.

  11. 11.

    Commission Implementing Regulation (EU) 2017/1469 of 11 August 2017 laying down a standardised presentation format for the insurance product information document details both the format and contents of the IPID, which are harmonised across the member States.

  12. 12.

    See Commission Delegated Regulation (EU) 2017/653 of 8 March 2017 laying down regulatory technical standards with regard to the presentation, content, review and revision of key information documents and the conditions for fulfilling the requirement to provide such documents.

  13. 13.

    Accordingly, the co-manufacturing regulation would be extended to include the following case: (i) an insurer agrees to supply an insurance product, and (ii) an insurance intermediary assembles this product with a product other than insurance, and (iii) the intermediary presents the assembled product to the customer as if it provided a full insurance guarantee.

  14. 14.

    See article 5, para. 2, of Directive 2005/29/EC.

  15. 15.

    The Product Disclosure Statement of FreindInsurance Cashback Bike Insurance Product outlines that: “Connections include You and each other person You are connected to through MyPlace for entire Calculation Months”.

  16. 16.

    Different rules are defined in practice. For instance, Lemonade gives back the money left over to specific causes the policyholder cares about (subject to board discretion and the company meeting certain financial standards).

  17. 17.

    Alternatively, the claims could be capped in this case. However, as stressed by EIOPA (2019), this solution introduces a potential inequality between first claims (entirely indemnified) and claims paid at the end of the year (potentially not indemnified at all).

  18. 18.

    For instance, \({r}_{g}\) is usually up to 10 in P2P groups (see friendinsurance.de and friendinsurance.au).

  19. 19.

    These assumptions can be violated in some specific contexts (for instance, the independence between number and cost in case of cat claims) and specific models have been developed for treating these issues (see, for instance, (Garrido et al. 2016)). For our purposes, we are neither interested in verifying if these assumptions are satisfied (or not) nor in identifying which is the best distribution for the claim size distribution.

  20. 20.

    In some contexts it is also defined as risk premium (see, for instance, (Daykin et al. 1994)). Actuarially fair insurance has an expected net pay-off of zero. From a consumer's point of view, an insurance contract is actuarially fair if the premiums paid are equal to the expected value of the compensation received. This expected value is, in turn, defined as the probability of the insured-against event occurring multiplied by the compensation received in the event of a loss.

  21. 21.

    Notice that in Braun et al. (2015), premiums charged by a stock insurer are defined as the difference between discounted expected aggregate loss and the so-called default put option of the stock insurer. In practice as well as in the actuarial literature, it is not so common to include the default option of the stock insurer (see, for instance, (Daykin et al. 1994), (Werner and Modlin 2016)). Capital allocation can obviously be introduced in pricing contracts (see, for instance, (Gründl and Schmeiser 2007)).

  22. 22.

    This criterion is typically applied by Lemonade, FriendInsurance and Axieme.

  23. 23.

    This criterion is typically applied by Guevara and Inspeer.

  24. 24.

    For instance, Axieme outlines on its website that the total premium is given by the premium paid to the third-party, the fees of the broker and the cashback.

  25. 25.

    For instance, Lemonade takes a flat 20 percent fee off the premium to cover salaries, running costs, and technology replacement.

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Appendix A: Details on the calculation of P2P premiums in different scenarios

Appendix A: Details on the calculation of P2P premiums in different scenarios

In formula (4), we defined the total fair premiums of the P2P portfolio as:

$${P}_{i,g}^{P2P}={P}_{i,g}^{F}+{P}_{i,g}^{TPI}+{P}_{i,g}^{TPI2}$$

where \({P}_{i,g}^{F}\) is the premiums’ portion kept in the mutual pool, \({P}_{i,g}^{TPI}\) is the fair premium paid to third-party insurance companies and \({P}_{i,g}^{TPI2}\) is used to provide an insurance coverage to cover minor claims in case the mutual pool is empty.

We denote with \({S}_{g}^{L}\) and \({S}_{g}^{S}\) the total aggregate claims amount, for the group \(g\), over and below the franchise limit \(t\), respectively. These two r.v.s are defined as:

$${S}_{g}^{L}=\left(\left(\sum_{i=1}^{{N}_{g}}{X}_{i,g}\right)|{X}_{i,g}>t\right)\, and\, {S}_{g}^{S}=\left(\left(\sum_{i=1}^{{N}_{g}}{X}_{i,g}\right)|{X}_{i,g}\le t\right).$$

Obviously, we have \(S_{g} = S_{g}^{L} + S_{g}^{S}\).

The total expected cost, considering both claims and possible cashback, can be defined as:

$$P^{P2P} = E\left( {\mathop \sum \limits_{g = 1}^{G} S_{g}^{L} } \right) + \mathop \sum \limits_{g = 1}^{G} E\left( {{\max}\left( {S_{g}^{S} - \mathop \sum \limits_{i = 1}^{{r_{g} }} P_{i,g}^{F} ,0} \right)} \right) + \mathop \sum \limits_{g = 1}^{G} E\left( {{\min}\left( {S_{g}^{S} ,\mathop \sum \limits_{i = 1}^{{r_{g} }} P_{i,g}^{F} } \right)} \right) + E\left( {CB} \right).$$
(A.1)

In formula (A.1), we have the following terms:

  • The expected value of aggregate amount that regards only claims larger than the limit. This amount is equal to the sum of fair premiums charged by the third-party insurance \({P}_{i,g}^{TPI}\) to each policyholder \(i\). In other words, it represents the total premium of a portfolio of homogeneous insurance contracts with a franchise equal to \(t\);

  • The expected value of the total amount considering only small claims (i.e. lower than the limit) and covering only the case of an empty pool. It represents the fair premium of the specific coverage \({P}_{i,g}^{TPI2}\), aggregated at portfolio level (i.e., the sum of premiums for each group);

  • The expected values of claims covered by the pool. For each group \(g\), this amount is upper bounded by the initial amount placed in the pool \(\sum_{i=1}^{{r}_{g}}{P}_{i,g}^{F}\);

  • The expected cashback. This amount is obviously related to the cashback rule defined by the entity managing the P2P insurance and it will be explored subsequently.

In formula (A.1), we can focus on the second and third terms

$$\sum\limits_{g=1}^{G}E(\mathrm{m}\mathrm{a}\mathrm{x}({S}_{g}^{S}-\sum_{i=1}^{{r}_{g}}{P}_{i,g}^{F},0))+\sum\limits_{g=1}^{G}E(\mathrm{m}\mathrm{i}\mathrm{n}({S}_{g}^{S},\sum_{i=1}^{{r}_{g}}{P}_{i,g}^{F}))=\sum\limits_{g=1}^{G}E\left(\mathrm{max}\left({S}_{g}^{S},\sum_{i=1}^{{r}_{g}}{P}_{i,g}^{F}\right)\right)+\sum\limits_{g=1}^{G}E(\mathrm{m}\mathrm{i}\mathrm{n}({S}_{g}^{S},\sum_{i=1}^{{r}_{g}}{P}_{i,g}^{F}))-\sum\limits_{g=1}^{G}\sum_{i=1}^{{r}_{g}}{P}_{i,g}^{F}=\sum\limits_{g=1}^{G}E\left({S}_{g}^{S}+\sum_{i=1}^{{r}_{g}}{P}_{i,g}^{F}\right)-\sum\limits_{g=1}^{G}\sum_{i=1}^{{r}_{g}}{P}_{i,g}^{F}=\sum\limits_{g=1}^{G}E\left({S}_{g}^{S}\right).$$

Given the linearity of the mean, we can rewrite formula (1) as:

$${P}^{P2P}=E\left(\sum_{g=1}^{G}{S}_{g}^{L}\right)+\sum\limits_{g=1}^{G}E\left({S}_{g}^{S}\right)+E\left(CB\right)=E\left(S\right)+E\left(CB\right)= P+E\left(CB\right),$$
(A.2)

where in the last step we have assumed that the expected aggregate amount of claims \(E\left(S\right)\) is not affected by the model. In other words policyholders file the same claims in either a P2P model or a traditional stock insurer model.

Different criteria can be set up in order to assess the expected value of the cashback. We provide two different alternatives:

  1. 1.

    Any positive amount remaining in the mutual pool is paid back to the policyholders of the group (or to a charity). In this case, we have:

    $$E(CB)=\sum\limits_{g=1}^{G}\left(\sum_{i=1}^{{r}_{g}}{P}_{i,g}^{F}-E\left(min\left({S}_{g}^{S},\sum_{i=1}^{{r}_{g}}{P}_{i,g}^{F}\right)\right)\right);$$
    (A.3)
  2. 2.

    To each policyholder in the group (or to a charity) is paid the difference, if positive, between the Potential Maximum Cashback (\(PMCB_{i,g}\)), defined by the entity managing the P2P insurance, and the total claim payments related to claims made by policyholders in the group

    $$E\left( {CB} \right) = \mathop \sum \limits_{g = 1}^{G} \left( {\mathop \sum \limits_{i = 1}^{{r_{g} }} PMCB_{i,g} - E\left( {min\left( {S_{g}^{{}} ,\mathop \sum \limits_{i = 1}^{{r_{g} }} P_{i,g}^{F} } \right)} \right)} \right).$$
    (A.4)

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Clemente, G.P., Marano, P. The broker model for peer-to-peer insurance: an analysis of its value. Geneva Pap Risk Insur Issues Pract 45, 457–481 (2020). https://doi.org/10.1057/s41288-020-00165-8

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Keywords

  • InsurTech
  • Distribution of insurance products
  • Peer-to-peer insurance
  • Premium rating
  • Insurance broker
  • Insurance regulation