A Study on the Design and Pricing of Adolescent Mental Health Insurance Products Based on Adjusted Rates

. In recent years, with the frequent occurrence of adolescent suicide, the topic of adolescent mental health has attracted special attention. The insurance products against this risk need to be studied. In this paper, based on an investigation of students and parents in five junior and senior high schools in Shandong Province, we design the adolescent mental health insurance product that meets the market demand and design additional insurance to protect against the risk induced by sudden accidents. The premium pricing system based on mental health status (MHSBI) is constructed with adjusted rates. The total premiums are in line with the applicants’ willingness to pay. This paper improves the deficiencies of insurance research about adolescent mental health, and provides theoretical support for the introduction of such insurance products.


Introduction
The recent incident of Hu Xinyu, a high school student in Jiangxi, who hanged himself, touched the heartstrings of millions of netizens and once again aroused the public's concern about the mental health of adolescents [1]. The Chinese National Mental Health Development Report (2019-2020) released by the Institute of Psychology of the Chinese Academy of Sciences shows that the detection rate of major depression is 7.4%, and adolescent psychological problems show a trend of low age [2]. In July 2021, the General Office of the Ministry of Education issued the Notice on Strengthening the Management of Students' Mental Health, clearly proposing "to do a good job of mental health assessment " [3], it is urgent to ensure the mental health of adolescents with the power of all sectors of society.
According to our survey, Chinese insurance industry has formed two main types in the market, personal health insurance and property insurance. However, adolescent mental health insurance products are still in a blue ocean market. Considering that the current domestic psychological counseling fees are too confusing and an industry standard system has not yet been formed [4]. It is important to design adolescent mental health insurance to reduce the risk of families bearing high psychological treatment costs and to provide diversified insurance services to enhance policyholders' awareness and prevention of mental illness [5].

Investigation implementation
This paper conducted an in-depth questionnaire survey on students and their parents in five middle and high schools, including Gaozhuang Central Middle School in Laiwu District, Jinan City, Shandong Province, Experimental Middle School, Fengcheng High School, and Gaotang County Second Middle School in Liaocheng City, Shandong Province, respectively. Among them, 713 questionnaires were collected from the investigation of adolescents, and 710 were valid, with an effective rate of 99.58%. A total of 564 questionnaires were collected from the survey of parents, and 559 were valid, with an effective rate of 99.11%.

Investigation results and analysis
The survey used SPSS 10.0 software to clean the questionnaire data, and used descriptive statistics, correlation coefficient and variance to conduct statistical analysis.
According to the investigation results, one quarter of adolescents have poor psychological selfawareness. And the treatment of psychological discomfort is limited to self-healing with low effectiveness.
Meanwhile, parents pay insufficient attention to the mental health of adolescents. And the mental health education in schools fails to achieve full coverage.
In terms of parents' views on mental health insurance, parents have a strong desire to adolescent mental health insurance, expecting to pay 270 RMB.

Design inspiration
In terms of premium setting, based on parents' willingness to take out mental health insurance and the expected payment, the basis of premium design is derived as 250-300 RMB. In terms of insurance service content design, based on the research results, the insurance is designed around "daily psychological care and aftercare psychological treatment" [6], and this insurance considers home school-enterprise cooperation to jointly support insurance to create value for adolescents.

Applicable objects
According to the World Health Organization's definition of adolescents (i.e. 10-19 years old) [7] which shows that the prevalence of mental illness is significantly higher in junior and senior high school individuals than in other stages, 13 to 18 years old is chosen as the applicable age range. Also, the insured should mental healthy tested after MMHI-60.

Coverage
Considering that there are many major risk events that may induce mental health disorders in addition to illnesses, the insurance is divided into primary and additional insurance to cover medical expenses and unexpected event losses respectively for one year.

Pricing of adolescent mental health insurance product
Based on the actuarial principles of non-life insurance, according to the principle of matching insurance companies' underwriting costs, risk taking and insurance rates, and with the introduction of the pricing idea of rate adjustment by UBI [8] (commercial auto insurance based on driving behavior), the MHSBI (Mental health status based insurance) pricing model is used for adolescent mental health insurance.
Premium components: total premium = adolescent mental health medical premium + adolescent accident premium.

Determination of MHSBI premium
Youth mental health medical premium = base premium × rate adjustment factor. The formula is , where is the youth mental health medical premium, is the base premium, and is the rate adjustment factor.

Base premium
The base premium is the amount of insurance multiplied by the base premium rate, i.e. , where represents the base premium, represents the amount of insurance, and represents the base premium rate. (1) Amount of insurance The insurance amount consists of the medical benefit and the service value , i.e.
. Among them, the medical benefit can be divided into two parts: the cost of psychological testing and the cost of treating psychological problems . The cost of psychological testing is determined by looking up the package cost of psychological counseling for adolescents by Qingdao psychological counseling institutions on the Meituan software and taking the average value of 570 yuan as the cost of a single test, i.e.
. For the cost of treatment of psychological problems, a total of 1666 cases with complete information on the first visit to a hospital's child and adolescent psychological clinic [9] between 2001 and 2010 were selected by searching the literature, and those cases aged 12 to 18 were selected for diagnostic classification by the International Classification of Diseases standard ICD-10 [10]. Then according to the serious problem of mental illness, all the symptoms are divided into severe, moderate, mild three categories. 6.9 per cent were classified as severe, 34.2 per cent as moderate and 58.9 per cent as mild.
The formula for calculating the cost of treatment for psychological problems is , which is the sum of the product of the probability of each disease category and its average treatment cost, and the result is calculated as RMB 15,329.77. Then the medical benefit is RMB 15,899.77. The cost of special services provided by this product mainly includes real-time psychological assessment, two psychological counseling sessions, hospital green channel and school lectures during the one-year insurance period. It is estimated that the cost of two psychological counseling sessions is roughly RMB 1,000 and the cost of other services is RMB 200 per person, totaling RMB 1,200. Then the total insurance amount is RMB 17,099.77.
(2) Determination of the benchmark premium rate The benchmark premium rate is determined by the benchmark pure premium rate and the additional cost rate, i.e.
, where is the benchmark pure premium rate and is the additional cost rate. The benchmark pure premium rate can be calculated from the formula , where is the prevalence of psychological problems among adolescents and is the proportion of adolescents with psychological problems who seek medical treatment. By looking at the results of the National Child and Adolescent Mental Disorders Flow Survey Report for 2021 and data from related literature, we can obtain . Then the benchmark pure premium rate is 0.0148. The additional cost rate is uniformly 0.35 during the pilot period. Therefore, the calculated benchmark premium rate is determined to be 0.0228.

Determination of rate adjustment factor
The rate adjustment factor is multiplied by the no-claims preference factor, the independent underwriting factor and the independent channel factor, i.e. . The no-claims preference factor is risk-graded according to the historical number of teenagers' insurance occurrences, and each level corresponds to the corresponding no-claims preference factor as shown with a floating range of [0.8,2.0]. No claims preference factor set to 0.8 if no previous claims have been incurred; in case of one previous claim, the no-claims preference factor is set to 1.0; in case of two previous claims, the no-claims preference factor is set to 1.5; for more than two prior claims, the no-claims preference factor is set to 2.0.
The independent underwriting coefficient was determined by the hierarchical analysis method to assess the psychological state of the insured. Among them, the psychological scale was Chinese Middle School Students' Mental Health Scale (MMHI-60). The weights of each index were determined by the hierarchical analysis method as shown in Table 1. The above indexes of the insured are scored with 1, 2 and 3 points respectively. The higher the score is, the better the situation is. The comprehensive score of the insured is the sum of the product of each index score and weight. The mental health status of the applicant is determined according to the comprehensive score, so as to determine the independent underwriting coefficient. Table 2 shows the corresponding relationship between the comprehensive score and the independent underwriting coefficient. The independent channel coefficient is related to the sales channel of the insurer. If the insured buys through the school group, then ; If the insured purchases it by himself, then .

Determination of adolescent accident premium
The additional insurance covers psychological problems caused by major accidents of teenagers. Its premium pricing can refer to other one-year children's accident insurance on the market. For this product, the one-year quotation of children's accident insurance issued by some insurance companies with similar insurance liability is selected as reference to determine the premium. And the average value of 65.25 yuan is taken as the premium of additional insurance of this product.
In summary, the total premium is determined as shown in Table 3.

Conclusions
Based on an investigation of students and parents, this paper designs the content of adolescent mental health insurance products. Combining the clinic data of Xiao Lijun et al. from 2001 to 2010, a mental health status-based premium pricing system (MHSBI) is constructed with a setting of adjusted rates to determine the total premium for each category.