CN109447831A - A kind of medical insurance Contract Design method based on wearable device - Google Patents

A kind of medical insurance Contract Design method based on wearable device Download PDF

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CN109447831A
CN109447831A CN201811622957.4A CN201811622957A CN109447831A CN 109447831 A CN109447831 A CN 109447831A CN 201811622957 A CN201811622957 A CN 201811622957A CN 109447831 A CN109447831 A CN 109447831A
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CN109447831B (en
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陈艳姣
邱晚玉
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Wuhan University WHU
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Abstract

The medical insurance Contract Design method based on wearable device that the present invention relates to a kind of.User is divided into different user types according to its different easy sick degree.For different type user, the contract that insurance company has formulated different exercise level and insurance premium is selected for client.Since the asymmetry of information namely insurance company are to the degree of understanding of user privacy information, three kinds of different situations: Complete Information, weak imperfect information, strong imperfect information are considered.Under three circumstances, which can promote different types of user to select its corresponding exercise level and charge.Go out Contract Mechanism finally by correlation theory Derivation.Contract Mechanism excitation user takes exercise and maximizes the effectiveness of insurance company.

Description

A kind of medical insurance Contract Design method based on wearable device
Technical field
The invention belongs to the designs of the Contract Mechanism of medical insurance, in particular to a kind of medical insurance based on wearable device Contract Design method.
Background technique
In recent years, many field development based on wearable device are very swift and violent, especially personalized health management.It is expected that By 2019, the market value of wearable device was up to 25,000,000,000 dollars.Wearable device can be used to monitor different classes of Health and fitness information: heart rate, breathing and step number.Using wearable device, the fortune of user is can be monitored in real time in insurance service provider Emotionally condition.Based on this, insurance service provider has carried out related research and development: motivating user to take exercise by discount offered insurance premium, makes It obtains healthier life style.
Contract theory, which is usually used to, solves the unbalanced relevant issues of information.It is widely used in economy and computer Network field, such as: frequency spectrum share, D2D communication, interference control and Wi-Fi price etc..The single frequency spectrum owner passes through quality Its frequency spectrum is sold to secondary user by price contract.Contract theory can also be used for D2D communication, provide excitation for it.Multidimensional contract reason Overall utility is maximized by be used to analyze amount of data optimal and subscription charge.
Summary of the invention
The present invention provides a kind of medical insurance contract based on wearable device and sets aiming at the deficiencies in the prior art Meter method.
To achieve the goals above, a kind of medical insurance Contract Design side based on wearable device designed by the present invention Method, it is characterised in that:
User group is investigated, according to insurance service provider to the degree of understanding of user information, scene point is carried out to user Class；
A series of insurance contract is formulated according to different scenes, which includes the insurance premium and user that user pays The relationship of exercise level, the insurance premium by providing the user with discount promote user to take exercise；
User selects corresponding insurance contract item according to the type of oneself.
Further, the scene classification includes:
Complete Information: insurance service provider is fully apparent from the type and number of each user；
Weak Complete Information: insurance service provider does not know the concrete type of each user, it is clear that user have it is more The quantity of few seed type and each type user；
Strong Complete Information: insurance service provider does not know the particular number of each type user, but knows total use Amount amount and user belong to the probability of concrete type.
Further, the insurance contract of the Complete Information scene, which is subject to, realizes maximization insurance service quotient effectiveness Then.
Still further, under the Complete Information conditional scene, the formulation mode of insurance contract specifically:
The effectiveness of the insurance service provider are as follows:
Wherein, α is the unit cost that insurance service provider monitoring user takes exercise, and β represents the range of insurance covering.C generation Table user go the unit of hospital to spend.ρkIt is that user selects exercise level for YkThe premium for needing to pay；The effectiveness needs to meet Constraint condition be: individual rationality related constraint: each type user selection insurance premium and exercise level will make its effect With being not less than 0, can be indicated with formula are as follows: M- (1- β) cvk(1-Yk)2-ρk≥0。
It recycles and polynary extreme value correlation theory is asked to find out Optimal Contract.
Still further, the insurance contract of the weak Complete Information scene selects kth item with the user for meeting kth seed type Contract is criterion.
Still further, under the weak Complete Information scene, the formulation mode of insurance contract specifically:
Following three conclusions are combined first:
(1)1≥ρ1≥ρ2≥…ρK>=0 and 1 >=Y1≥Y2≥…YK>=0, i.e. the insurance to be paid of the first type of user Take the insurance premium to be paid of user exercise level corresponding with its that exercise level corresponding with its is respectively greater than second of type, The rest may be inferred；
(2)M-(1-β)cv1(1-Y1)2-ρ1>=0: the income of the first type of user should be not less than 0；
(3)
ρk-(1-β)c[(1-Yk+1)2-(1-Yk)2]vk≤ρk+1≤ρk-(1-β)c[(1-Yk+1)2-(1-Yk)2]vk+1；
Under weak imperfect information scene, the target of insurance contract is equally the effectiveness for maximizing insurance service provider:
The constraint condition that effectiveness needs meet is: compatible incentives are theoretical, i.e., the user of kth seed type selects k-th of conjunction Effectiveness with project selects the effectiveness of remaining k-1 contract item not less than him, can be indicated with formula are as follows:
M-(1-β)cvk(1-Yk)2-ρk≥M-(1-β)cvk(1-Yi)2-ρi,K ∈ [1, K], the formula are also required to meet Individual rationality constraint condition；
Then the method optimal using sequence, first finds out optimal insurance premium, finally finds out optimal exercise journey Degree.
Still further, in strong imperfect information scene, the probability density function of user are as follows:
Wherein, γkThe probability that user belongs to kth seed type is represented, therefore,nkRepresent kth seed type The number of user, N represent the total number of persons of user；In the insurance contract of the strong imperfect information scene, probability density function can To be construed to the probability scenarios of different type user number distribution, the user of kth seed type is recycled to select subject to kth item contract Then.
Still further, under the strong imperfect information scene, the formulation mode of insurance contract specifically: described strong endless The target of full information is:
The constraint condition that formula needs meet is: individual rationality and compatible incentives, according in weak Complete Information scene Three conclusions, it is assumed that the exercise level of known preferred solves optimal insurance premium, is then solved according to the insurance premium found out optimal Exercise level, finally solve the Optimal Contract under strong imperfect information.
The present invention has the advantages that
The present invention mainly proposes an Incentive contracts mechanism, and enabling insurance service provider is different types of user Formulate reasonable insurance premium and exercise level.The contract frame of proposition considers the unbalanced factor of information, so that last contract Mechanism can adapt to different use occasions.It has found out optimal contract to develop programs, has maximized the effect of insurance service provider With.
Detailed description of the invention
Fig. 1 is flow chart of the invention.
Fig. 2 is that the unit of insurance service provider is spent to insurance service provider effectiveness, the total effectiveness of user, Yi Jisan The influence of the amount of exercise total to user under the different situations of kind.
Fig. 3 is that user spends in the unit of hospital to insurance service provider effectiveness, and the total effectiveness of user and three kinds are not With the influence of amount of exercise total to user under situation.
Fig. 4 is the comparison of Optimal Contract under three kinds of different situations.
Fig. 5 is the specific value table based on Fig. 4 Optimal Contract.
Specific embodiment
The present invention is described in further detail in the following with reference to the drawings and specific embodiments:
In the present invention, a kind of medical insurance Contract Design method based on wearable device is proposed: for different type User formulate corresponding exercise level and charge.Study the insurance mechanism design based on wearable device.Insurance service provides Quotient provides the user with wearable device to monitor the daily routines of user, while collecting the different insurance premium of user.User's is strong Health situation can be improved by reinforcing taking exercise.There are two the challenges of aspect for one effective incentive mechanism of design: first, insurance Service provider and user have the characteristics that selfish and rationality, the two are intended to maximize the effectiveness of oneself.Such as: insurance clothes Business provider wishes that user is as far as possible more and takes exercise to reduce health care costs still and wish to collect more premiums, user Ze Xi It hopes exercise appropriate and pays a small amount of premium, there is the conflict of interest between them.Second, the unbalanced problem of information.To the greatest extent Pipe insurance service provider can obtain the exercise level of user by wireless device, but the health status of user itself is hidden Personal letter breath.Insurance service provider is that different types of user formulates insurance contract in the case where not knowing user health situation It has any problem.
So in the present invention, consider the scene of Complete Information first: insurance service provider knows each user's Type.Then consider imperfect information: insurance service provider does not know the concrete type of each user.Design a kind of contract Mechanism promotes user to automatically select its insurance premium and exercise level.In order to achieve this goal, compatible incentives and individual are described Rationality correlation theory solves Optimal Contract in turn.
In view of the deficiencies of the prior art, the present invention proposes an Incentive contracts mechanism.The specific method is as follows:
User group is investigated, according to insurance service provider to the degree of understanding of user information, scene point is carried out to user Class；
A series of insurance contract is formulated according to different scenes, which includes the insurance premium and user that user pays The relationship of exercise level, insurance service provider is by providing the user with the insurance premium of discount to promote user to take exercise, finally Maximize the effectiveness of oneself.
User selects corresponding insurance contract according to the type of oneself.
Insurance service provider designs a series of medical insurance contracts, the specific steps are as follows:
According to insurance service provider to the degree of understanding of user information, scene classification is carried out to user, including believe completely Breath, weak incomplete complete information and strong imperfect information.
Complete Information: in reference background: assuming that 1 insurance service provider and N number of user.The type of user i indicates For vi, represent the sick degree of user i, viIt is bigger, illustrate that user is more liable to illness.And the type for assuming user is oneself Privacy information.Without loss of generality, it is assumed that user i sick probability is: P (yi|vi)=vi(1-yi)2.Wherein yiRepresent user i Exercise level.Equally, yiIt is bigger, it is more to illustrate that user i takes exercise.Although this formula is very simple, use can be expressed Temper the relationship between its health degree in family.User's exercise level is higher, then a possibility that its is sick is lower.Assuming that there is K The user of seed type constitution.The utility function of each type user can be indicated are as follows: uk=M- (1- β) cvk(1-Yk)2-ρk.Its In, M represents the assets of user.β represents the range of insurance covering.C represents user and the unit of hospital is gone to spend.ρkIt is user's choosing Selecting exercise level is YkThe premium for needing to pay.So the utility function of user can be construed to the cost that its assets subtracts hospital Subtract its premium paid.Its contract form are as follows:Under Complete Information, insurance service provider It is fully apparent from the type of each user.
Weak imperfect information: insurance service provider does not know the concrete type of each user, it is clear that user has The quantity of how many seed type and each type user.Needing to design a contract makes the user of kth seed type select kth item Contract.
Strong imperfect information: on the basis of weak imperfect information, insurance service provider does not know each type user Particular number, but know that total number of users and user belong to the probability of concrete type.Therefore, the probability density letter of user Number can indicate are as follows:
Wherein, γkRepresent the probability that user belongs to kth seed type.Therefore,nkRepresent the number of the user of kth seed type.N generation The total number of persons of table user.So probability density function can be construed to the probability scenarios of different type user number distribution.
User selects suitable medical insurance contract according to the privacy type of oneself, the specific steps are as follows:
Complete Information: the effectiveness of each type user is all 0.It is 0 that low sick degree user, which selects exercise level, insurance premium With lower, high sick degree user selects exercise level to be greater than 0, and insurance premium is higher.
Weak imperfect information: as the sick degree of user increases, the insurance premium and exercise level that user pays gradually increase Greatly.The kth item of kth (1≤k≤K) seed type user selection contract.
Strong imperfect information: similar with weak imperfect information, each user type selects the respective items of contract.
Specific step is as follows for the formulation of Complete Information contract:
Step 1.1: under Complete Information scene, target is to maximize the effectiveness of insurance service provider, can be indicated are as follows:Wherein, α is the unit that insurance service provider monitoring user takes exercise Cost.Maximizing the constraint condition that insurance service provider effectiveness needs meet is: individual rationality related constraint: each type The insurance premium and exercise level of user's selection will make its effectiveness not less than 0.It can be indicated with formula are as follows: M- (1- β) cvk(1- Yk)2-ρk≥0.Under Complete Information scene, according to former work related conclusions: the effectiveness of the user of each type is all 0.? On the basis of this, need to solve Optimal Contract to maximize the effectiveness of insurance service provider.
Step 1.2 implementation: extreme value correlation theory is asked to find out Optimal Contract with polynary.
The best contract of step 1.3: it by the derivation of equation, finally concludes that for low sick degreeUser:For high sick degree User:
The insurance contract of weak imperfect information is formulated, the specific steps are as follows:
Step 2.1: before solving imperfect information scene, according to IC (Incentive Compatibility) and IR (Individual Rationality) two correlation theories knowledges derive three important conclusions:
(1)1≥ρ1≥ρ2≥…ρK>=0 and 1 >=Y1≥Y2≥…YK≥0.That is the insurance to be paid of the first type of user Take the insurance premium to be paid of user exercise level corresponding with its that exercise level corresponding with its is respectively greater than second of type, The rest may be inferred.
(2)M-(1-β)cv1(1-Y1)2-ρ1>=0: the income of the first type of user should be not less than 0.
(3)
ρk-(1-β)c[(1-Yk+1)2-(1-Yk)2]vk≤ρk+1≤ρk-(1-β)c[(1-Yk+1)2-(1-Yk)2]vk+1
.Under weak imperfect information scene, it is equally the use for maximizing insurance service provider that insurance, which sets objectives:The constraint condition that its needs meets is: compatible incentives are theoretical, i.e. kth The user of seed type selects the effectiveness of k-th of contract item to select the effectiveness of remaining k-1 contract item not less than him.Use formula It can indicate are as follows: M- (1- β) cvk(1-Yk)2-ρk≥M-(1-β)cvk(1-Yi)2-ρi,K ∈ [1, K].Therefore, the first type Type user will select the first item of contract, and so on, K seed type user can select K of contract.Equally, this Formula is also required to meet individual rationality constraint condition.
Step 2.2: implementation: using the method that sequence is optimal, first finding out optimal insurance premium, then find out Optimal exercise level.
Step 2.3: be finally concluded that: best insurance premium is:
Best exercise level is:Wherein,
The insurance formulating method of strong imperfect information, the specific steps are as follows:
Step 3.1: under strong imperfect information scene, objective function are as follows:
Most The constraint condition that bigization formula needs meet is: individual rationality and compatible incentives.The three important knots proposed according to step 2.1 By needing to solve Optimal Contract.
Step 3.2: implementation method: assuming that the exercise level of known preferred solves optimal insurance premium, then basis is found out Insurance premium solve optimal exercise level.The Optimal Contract under strong imperfect information can finally be solved.
Step 3.3: finally, the Optimal Contract found out is:
Finding out optimal exercise level is:Wherein,
The embodiment of the present invention operates on Matlab, and insurance is taken following with the results show information is unbalanced Be engaged in provider and user effectiveness influence, assume in Fig. 2
N=100, c=0.6, α=0.2,0.4,0.6,0.8,1.0, β=0.5, M=2.
Assume in Fig. 3
N=100, α=0.5, c=0.2,0.4,0.6,0.8,1.0, β=0.5, M=0.5.
Assume in Fig. 4
N=20, c=0.6, α=0.2,0.4,0.6,0.8,1.0, β=0.5, M=0.5.
Fig. 2 Fig. 3 assumes there are 3 kinds of different types of users: 0.2,0.5,0.8.Assume there are 5 kinds of different types of use in Fig. 4 Family: 0.1,0.3,0.5,0.7,0.9.
Assuming that the number of user obeys Joint Gaussian distribution.Corresponding different scene, finds out the list of insurance service provider Position, which is spent, spends the influence to the effectiveness and user's overall utility of insurance service provider in the unit of hospital with user.Meanwhile Solve the sum of various types user exercise level under different situations.Finally, having found out the concrete form of contract.
Analysis of experimental results:
Fig. 2: assuming that the unit cost that insurance service provider is used to monitor user's exercise is: 0.2,0.4,0.6,0.8, 1.0.Observe that the unbalanced effectiveness to insurance service provider and user of information plays an important role.When insurance service provides When quotient has the Complete Information of user, its higher profit when can be obtained by contract compared to imperfect information.When insurance takes The information that business provider is known is fewer, then the effectiveness of insurance service provider is fewer.Because user and insurance service provide Quotient has the conflict of interest, thus the effectiveness of user just obtain it is more.Under Complete Information, the effectiveness of user is 0, but endless Under full information, the effectiveness of user is greater than 0.It is compared with Complete Information, user needs more exercises maximum under imperfect information Change the effectiveness of oneself.
Fig. 3: assuming that user goes the unit of hospital to spend are as follows: 0.2,0.4,0.6,0.8,1.0.When user goes the unit of hospital Expense increases, and insurance service provider has to pay high medical expense, so that the effectiveness of insurance service provider be made to subtract It is few.On the contrary, the effectiveness of user will increase in the case where imperfect information, because the insurance premium in contract can cured with user The increase of institute's unit costs and reduce, meanwhile, the best exercise level in contract also can be lower.In weak imperfect information situation Under, when user go hospital unit costs it is relatively low when, the total effectiveness of user be it is increased, when expense is relatively high, Yong Huzong Effectiveness be reduce.Main reasons is that best exercise level can also compare when user goes the unit costs of hospital relatively low It is low, by tempering their health degree of promotion therefore reducing their sick chances.However, the unit when hospital spends ratio When higher, user can spend more money purchase medical insurances and exercise, therefore reduce their effectiveness.
Fig. 4 compares the Optimal Contract under three kinds of different scenes.Obtain the unbalanced best exercise for affecting user of information Degree and insurance premium.Insurance service provider knows that the information of user is fewer, more beneficial to user.When the type of user increases When, the best exercise level of user also will increase because the bigger user of type is more liable to illness, more needing by more Exercise maximize his income.For imperfect information compared to Complete Information, user needs more take exercise to maximize him Effectiveness.Unbalanced due to information, the best insurance premium of user is discrepant under three circumstances.It is similar, work as guarantor Dangerous service provider knows the more information of user, and the effectiveness of user will be lower.It can be observed that the type as user is lower When, user can pay more insurance premiums under the scene of Complete Information.
Fig. 5 is the numeric form of Fig. 4.Type one, two, three, four, five are respectively as follows: 0.1,0.3,0.5,0.7,0.9.Numerical value Bigger, user is more liable to illness.
Above embodiments are merely to illustrate design philosophy and feature of the invention, and its object is to make technology in the art Personnel can understand the content of the present invention and implement it accordingly, and protection scope of the present invention is not limited to the above embodiments.So it is all according to It is within the scope of the present invention according to equivalent variations made by disclosed principle, mentality of designing or modification.

Claims (8)

1. a kind of medical insurance Contract Design method based on wearable device, it is characterised in that:
User group is investigated, according to insurance service provider to the degree of understanding of user information, scene classification is carried out to user；
A series of insurance contract is formulated according to different scenes, which includes that the insurance premium that user pays and user take exercise The relationship of degree, the insurance premium by providing the user with discount promote user to take exercise；
User selects corresponding insurance contract according to the type of oneself.
2. the medical insurance Contract Design method according to claim 1 based on wearable device, it is characterised in that: described Scene classification includes:
Complete Information: insurance service provider is fully apparent from the type and number of each user；
Weak Complete Information: insurance service provider does not know the concrete type of each user, it is clear that how many kind of user The quantity of type and each type user；
Strong Complete Information: insurance service provider does not know the particular number of each type user, but knows total number of users Amount and user belong to the probability of concrete type.
3. the medical insurance Contract Design method according to claim 2 based on wearable device, it is characterised in that: described The insurance contract of Complete Information scene maximizes insurance service quotient effectiveness as criterion to realize.
4. the medical insurance Contract Design method according to claim 2 based on wearable device, it is characterised in that: described Under Complete Information conditional scene, the formulation mode of insurance contract specifically:
The effectiveness of the insurance service provider are as follows:
Wherein, α is the unit cost that insurance service provider monitoring user takes exercise, and β represents the range of insurance covering, and c represents User goes the unit of hospital to spend, ρkIt is that user selects exercise level for YkThe premium for needing to pay, N represent the total number of persons of user, vkFor user type；The constraint condition that effectiveness needs meet is: individual rationality related constraint: each type user selection Insurance premium and exercise level will make its effectiveness not less than 0, can be indicated with formula are as follows: M- (1- β) cvk(1-Yk)2-ρk>=0, Recycle it is polynary ask extreme value correlation theory to find out Optimal Contract, M represents the assets of user.
5. the medical insurance Contract Design method according to claim 4 based on wearable device, it is characterised in that: described The insurance contract of weak Complete Information scene selects kth item contract as criterion to meet the user of kth seed type.
6. the medical insurance Contract Design method according to claim 5 based on wearable device, it is characterised in that: institute It states under weak Complete Information scene, the formulation mode of insurance contract specifically:
Following three conclusions are combined first:
(1)1≥ρ1≥ρ2≥…ρK>=0 and 1 >=Y1≥Y2≥…YK>=0, i.e., the insurance premium to be paid of the first type of user and The insurance premium to be paid of user exercise level corresponding with its that its corresponding exercise level is respectively greater than second of type, according to this Analogize；
(2)M-(1-β)cv1(1-Y1)2-ρ1>=0: the income of the first type of user should be not less than 0；
(3)
ρk-(1-β)c[(1-Yk+1)2-(1-Yk)2]vk≤ρk+1≤ρk-(1-β)c[(1-Yk+1)2-
(1-Yk)2]vk+1；
Under weak imperfect information scene, the target of insurance contract is equally the effectiveness for maximizing insurance service provider:
The constraint condition that effectiveness needs meet is: compatible incentives are theoretical, i.e., the user of kth seed type selects k-th of contract Purpose effectiveness selects the effectiveness of remaining k-1 contract item not less than him, can be indicated with formula are as follows:
M-(1-β)cvk(1-Yk)2-ρk≥M-(1-β)cvk(1-Yi)2-ρi,K ∈ [1, K], the formula are also required to meet individual Rationality constraint condition；
Then the method optimal using sequence, first finds out optimal insurance premium, finally finds out optimal exercise level.
7. the medical insurance Contract Design method according to claim 6 based on wearable device, it is characterised in that:
In strong imperfect information scene, the probability density function of user are as follows:
Wherein, γkThe probability that user belongs to kth seed type is represented, therefore,nkRepresent the user's of kth seed type Number, N represent the total number of persons of user；In the insurance contract of the strong imperfect information scene, probability density function can be explained For the probability scenarios of different type user number distribution, the user of kth seed type is recycled to select kth item contract for criterion.
8. the medical insurance Contract Design method according to claim 7 based on wearable device, it is characterised in that: described Under strong imperfect information scene, the formulation mode of insurance contract specifically: the target of the strong imperfect information is:
The constraint condition that formula needs meet is: individual rationality and compatible incentives, according to three in weak Complete Information scene Conclusion, it is assumed that the exercise level of known preferred solves optimal insurance premium, then solves optimal forging according to the insurance premium found out Refining degree can finally solve the Optimal Contract under strong imperfect information.
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CN114401544A (en) * 2022-03-25 2022-04-26 武汉大学 Unmanned aerial vehicle communication network energy harvesting method and system based on contract theory

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CN106780052A (en) * 2017-01-10 2017-05-31 上海诺悦智能科技有限公司 Method and system are recommended in insurance service based on classification customer behavior analysis
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CN107767959A (en) * 2017-11-15 2018-03-06 平安健康保险股份有限公司 Health risk assessment method, apparatus and equipment based on character trait
CN108734593A (en) * 2018-05-15 2018-11-02 中国平安人寿保险股份有限公司 Life insurance is reported a case to the security authorities method, apparatus, computer equipment and readable storage medium storing program for executing

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CN114401544A (en) * 2022-03-25 2022-04-26 武汉大学 Unmanned aerial vehicle communication network energy harvesting method and system based on contract theory
CN114401544B (en) * 2022-03-25 2022-06-17 武汉大学 Unmanned aerial vehicle communication network energy harvesting method and system based on contract theory

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