29 July 2018
Decentralised insurance model
Abstract
With the development of sharing economy and decentralised platforms like Bitcoin and Ethereum the financial products decentralisation has been the focal point for some projects and studies in the blockchain world. In this paper, we build a decentralised insurance model based on our researches and experience in REGA Risk Sharing and evaluate the model parameters to prove that the decentralised insurance can be an alternative solution to the traditional insurance approach.
Keywords
Decentralised insurance, blockchain, smart contract, crowdsurance, valuation, marketing.
1. Introduction
The decentralised insurance or crowdsurance meaning people unite in communities to provide a guarantee of compensation for unexpected loss. Compared to traditional insurance, in crowdsurance there are no insurers, intermediaries and brokers, all the processes being controlled and managed by programs stored in blockchain and executed by a distributed virtual computer. The main question in this case is how to motivate people inside the community to use crowdsurance programs in the right way to provide the risk coverage and fight the fraud. Some people intensions and actions can be in opposition of these objectives but in the decentralised economy if most actors are motivated properly to bring value to the community then the outcome of the whole process will be inline with common goal.
There are two groups of people using crowdsurance program: A - people who join crowdsurance pool to get risk coverage and B - people who help the first group manage risks inside the crowdsurance pools. We will call the first group a crowdsurance community or community and the second one - experts. To join the crowdsurance community someone should buy a crowdsurance token (CST) and transfer a crowdsurance join amount to the crowdsurance token smart contract. To became an expert a person should buy a license, Risk Sharing Token (RST) and transfer an expert join amount to the RST smart contract. Funds collected in RST smart contract are using for crowdsurance product development and for the initial crowdsurance pools capitalisation. Inside the crowdsurance token smart contract there is three level pool structure: super pool, pools and sub pools. Each CST belongs to one sub pool that belongs to one pool and all pools included in super pool. The crowdsurance join amount is divided between different levels in there following way: 50% goes to sub pool, 20% to pool and 10% is transferred to super pool. The rest 20% is crowdsurance smart contract commission. A CST holder can activate the token to initiate the risk coverage period during which he/her can submit a claim to receive crowdsurance payment in case of unexpected event. The submitted claim will be processed by the crowdsurance program and will be submitted to an expert jury for final approval. For each outstanding claim the randomly selected jury will be created and experts will vote for the case using crowdsurance token smart contract. During the claim voting period (up to 48 hours) any jury member can review claim supported documents and vote in favour of payment or against it. The claim payment will be processed by the crowdsurance smart contract based on voting result and the CST holder could receive the claim payment if payment was approved by the jury. A part of the smart contract commission (3%) will go to the experts to compensate transaction fee and working time. If an expert was selected to vote but did not cast the vote during the voting period then he/her will not receive the compensation. Otherwise all other experts will receive expert commission even if they did not selected to vote. The crowdsurance smart token linked to the Risk Sharing Token through the super pool. The RST value will rise if the super pool balance will be more then a certain threshold at the end of risk coverage period as result of the experts performance. In the next section we will describe the crowdsurance model that explains an expert motivation to process claims and vote for the legitimate cases and decline the fraudulent ones. The model takes into account a community member satisfaction level for different voting outcomes.
2. The model
The model consists of crowdsurance token smart contract working through two risk coverage periods. Similar to [1] community member decision making to join crowdsurance pool is modelled using the the surplus the member obtain from the decentralised product experience. The surplus is the difference between a member’s valuation for the product and the amount he/she must transfer to join it. It’s assumed that a member joins the crowdsurance pool, if the offer yields a nonnegative surplus. Let’s assume that 
is the average risk coverage period for the community member that did not submit any claim. For a member who has submitted the claim in the first risk coverage period and has received the payment the product valuation for the next period should be more that the average one. From the other hand if claim was rejected then the valuation must be less. So, we can assume that for the member that has received the claim payment the crowdsurance contract lasts 
and the rejected claim results in 
periods. If 
is group of members who has submitted the claim then the super pool financial result after the two risk coverage period can be calculated by the following expression:
where 
is crowdsurance join amount and 
is the average super pool balance update due to the claim processing. To calculate we need to consider the following cases:
- the submitted claim
is legitimate one;
- the submitted claim
is fraudulent one.
In both cases we will have the following outcomes for the expert voting procedure:
the claim is approved by the jury and member will receive claim payment amount
the claim has beed declined by the jury and the member not receive any payment from the crowdsurance pool.
Based on assumption that the member product valuation will change he/her average risk coverage period we can say that for 
voting outcome will credit the super pool balance to 
and the 
will debit it 
. We also can assume that 
will bring the member product valuation surplus to 0 but it should not change the average crowdsurance period. Please note, that we are considering the crowdsurance model where all legitimate claims can be paid out using sub pool and pool funds and , voting outcomes are not using the super pool balance to pay claim in full or to return crowdsurance join amount . On another hand fraudulent claims can have negative impact on super pool balance due to the shortage of funds in corresponding sub pool and pool. Thereby 
outcome will change the super pool balance to 
and 
to 
where 
is probability of the fund shortage in sub pool and pool. The following table summarise described above outcomes:
|
Claim types / Voting results
|
D
|
J
|
Z
|
|
|
|
|
|
|
Legitimate - L
|
0.1Jx
|
0
|
-0.1Jy
|
|
|
|
|
|
|
Fraudulent - F
|
0.1Jx-Dp
|
-Jp
|
0
|
|
|
|
|
|
We suppose that for member submitted fraudulent claim voting results and 
does not change the average crowdsurance period on another hand if fraudulent case has been paid then the member will more probably join the next period to try cheat again.
Now we can calculate using the following expression:
Applying conditional probability theory, the above equation can be rewritten as:
where 
We should assume that number of fraudulent claims is much less then the number of legitimate one, so we are adding the following condition: 
to the expression 2 where 
. With this assumption we can try to calculate the probability of the funds shortage . If N is total number of claims, NL is number of legitimate 
claims and NF is fraudulent ones then 
and 
. In this case we can estimate 
with the following expression:
Suppose we a have tree level pool structure where K is number of sub pools and
is claims distribution between sub pools. For any distribution we have: 
and if there is 
for 
then we have the following condition 
. Thereby for any sub pool claim distribution we can have only one . In our model we еhave assumed that if for some claim distribution 
is true for all j then all claims from this distribution can be paid out using sub pool and pool funds without affecting the super pool balance. Thus to calculate the probability of event when claim payment affects super pool balance we need to calculate the number of claim distributions with one member 
. For such member we can have the following set of values 
and for any 
where 
we can have 
distributions . So the total number of distributions is 
and 
(3)
3. Model parameters valuation
Now we need to check that it’s possible to find where 
. Let’s consider the following expression 
where 
and 
where 
. If 
then 
and if 
then 
Consider the following outcome probabilities example
In this case 
and if 
then 
Suppose the total number of claims is 100 and number of sub pools 5 then 
and 
.
Let’s return to the definition of . Now we can see that if 
or 
. In our example 
and 
. Thus if 
.
If 
then we can assume that 
and all member who has submitted legitimate claim and did not received the payment left the crowdsurance pool after the first period. On another hand we can assume that all members that have received the approval have two periods and 
. Based on our example outcome probabilities we can see that for and . Please note then the minimum value for 
in our example that gives 
is and for we need 
or
.
4. Summary and conclusion
In the previous sections we have build crowdsurance model with expert performance function (2) that explain expert motivation to consider claims properly voting to legitimate ones and reject fraudulent attempts. Based on expression (2) we can see that if experts have decided to vote again all cases including legitimate ones then the value of expert performance function will become negative that brings decrease to RST token value. On another hand if experts have decided to approve all cases including fraudulent ones then this decision will change the risk balance in next crowdsurance period due to the fact that more fraud attempts will appear and the probability of pool / sub pool funds shortage will increase. Thus with increase of and 
the value of 
in (2) can became more substantial and again the expert performance will became negative.
We also have evaluated the model parameters using example for voting outcome distribution and have proved that there is not empty set of outcome distributions that gives realistic value to the model parameters . It’s save to assume that the average crowdsurance period will be around 1.1 and in our example distribution we check that for the value for expert performance function will be positive for all from 
.
Based on the above summary we can conclude that the decentralised insurance product with two group of people with different motivations connected thought blockchain program can be created and function to bring value to both groups. We hope that it will help crowdsurance to became an alternative solution for risk coverage and will change insurance landscape in the nearest future.
References
[1] Amir Gandomi and Saeed Zolfaghari, 2011 “Profitability of Loyalty Programs in th Presence of Uncertainty in Customers’ Valuations” Proceedings of the 2011 Industrial Engineering Research Conference
