Measuring medical inflation for health insurance portfolios in Belgium

Dhaene, Jan; Hanbali, Hamza

doi:10.1007/s13385-019-00200-6

Cited by 7 publications

(3 citation statements)

References 4 publications

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“…The following lemma presents the structure of the solutions to the extended HJB Equations ( 14) and (15). Because the proof is similar to that of Lemma 4.1 in [30], the details are omitted.…”

Section: The Policyholder's Best Response Strategymentioning

confidence: 99%

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Optimal Private Health Insurance Contract towards the Joint Interests of a Policyholder and an Insurer

Yang

Chen

2023

Mathematics

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This paper investigates the optimal private health insurance contract design problem, considering the joint interests of a policyholder and an insurer. Both the policyholder and the insurer jointly determine the premium of private health insurance. In order to better reflect reality, the illness expenditure is modelled by an extended compound Poisson process depending on health status. Under the mean–variance criterion and by applying dynamic programming, control theory, and leader–follower game techniques, analytically time-consistent private health insurance strategies are derived, optimal private health insurance contracts are designed, and their implications toward insurance are analysed. Finally, we perform numerical experiments assuming that the policyholder and the insurer calculate their wealth every year and they deposit their disposable income into the Bank of China with the interest rate being r=0.021. The values of other model parameters are set by referring to the data in the related literature. We find that the worse the policyholder’s health, the higher the premium that they pay for private health insurance, and buying private health insurance can effectively reduce the policyholder’s economic losses caused by illnesses.

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Section: The Policyholder's Best Response Strategymentioning

confidence: 99%

“…Ref. [15] studied the construction of medical inflation indexes and the formulation of premiums of lifelong health insurance. The above-mentioned studies were based on static or discrete-time frameworks; however, they cannot reflect a continuous change in illness information and health status.…”

Section: Introductionmentioning

confidence: 99%

Optimal Private Health Insurance Contract towards the Joint Interests of a Policyholder and an Insurer

Yang

Chen

2023

Mathematics

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“…Martinon et al 14 established a single‐period utility model for investigating the private health insurance problem. Dhaene and Hanbali 15 constructed medical inflation indexes and studied their application in the update premiums of lifelong private health insurance contracts. All these studies were carried out under the static or discrete‐time framework.…”

Section: Introductionmentioning

confidence: 99%

Optimal time‐consistent social health insurance and private health insurance strategy under a new health insurance framework

Yang

Chen

2022

Appl Stoch Models Bus & Ind

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A new continuous‐time health insurance framework is proposed to simultaneously determine the optimal social health insurance strategy and optimal private health insurance strategy. The social health insurance can cover both the expenditures of general illnesses and critical illnesses, while the private health insurance only covers the expenditure of critical illnesses. To reflect the inevitable connection between critical illnesses and general illnesses, we assume that the number of critical illnesses and the number of general illnesses are positively correlated. The policyholder's objective is to find an optimal time‐consistent social health insurance and private health insurance strategy so as to maximize the expected terminal wealth while minimizing the variance of the terminal wealth. Explicit solutions for the optimal time‐consistent health insurance strategy and the corresponding value function are obtained by employing the stochastic control technique. Finally, we numerically examine the influence of expenditure parameters on the optimal time‐consistent health insurance strategy, and also examine the effect of the health insurance on the policyholder. The results reveal the similarities and differences between social health insurance and private health insurance, which provide insightful guidance for health insurance practice in reality.

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Once covered, forever covered: The actuarial challenges of the Belgian private health insurance system

et al. 2019

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The Belgian Law of 20 July 2007 has drastically changed the Belgian private health insurance sector by making individual contracts lifelong with the technical basis (i.e. actuarial assumptions) fixed at policy issue. The goal of the Law is to ensure the accessibility to supplementary health coverage in order to protect policyholders from discrimination and exclusion, essentially when these operate on the basis of age. Due to the unpredictable nature of medical inflation risk and the difficulty to model future increases of health claims, the legislator introduced medical indices together with a specific updating mechanism, which aim at establishing standardized and fair premium adjustments across the sector. This paper considers two major issues of the current Belgian system. The first one is related to the transferability of the reserves, whereas the second one is related to age-discrimination. We discuss these issues and their interplay, and we address the conflict between the goal of the Law and the practical problems arising in the light of the actuarial techniques.

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Measuring medical inflation for health insurance portfolios in Belgium

Cited by 7 publications

References 4 publications

Optimal Private Health Insurance Contract towards the Joint Interests of a Policyholder and an Insurer

Optimal Private Health Insurance Contract towards the Joint Interests of a Policyholder and an Insurer

Optimal time‐consistent social health insurance and private health insurance strategy under a new health insurance framework

Once covered, forever covered: The actuarial challenges of the Belgian private health insurance system

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