Journal of Mathematics and Modeling in Finance

Optimal Coverage Limit Design for Health Insurance under Stochastic Claims and Policyholder Coverage Selection

Articles in Press

Document Type : Research Article

Authors

Ramazan Rezazadeh 1
Amir Teimour Payandeh Najafabadi 1
Kaled Masoumifard 2

1 Department of Actuarial Science, Faculty of Mathematical Sciences, Shahid Beheshti University, Evin, Tehran, Iran.

2 Department of Statistics & Actuarial Science, Stellenbosch University, Stellenbosch, South Africa.Stellenbosch, South Africa.

10.22054/jmmf.2026.92687.1287
Abstract
Determining optimal coverage limits is a fundamental problem in health insurance, as insurers must balance profitability, policyholders’ preferences, and risk exposure under uncertain claim experience. Existing studies generally optimize coverage limits by considering either claim uncertainty or policyholder behavior, while their combined effects have received limited attention. To address this gap, this paper develops a mathematical framework for the optimal design of multiple health insurance coverage limits by jointly incorporating stochastic claim frequencies and policyholders’ coverage selection probabilities. The insurer’s decision problem is formulated as the maximization of an exponential utility function subject to a probabilistic risk constraint defined by a loss threshold t and a confidence level θ. Using probabilistic bound theory, the stochastic optimization problem is transformed into an equivalent convex optimization problem that can be efficiently solved using the Lagrange multiplier method. The resulting optimality conditions lead to a system of nonlinear equations, for which the existence and uniqueness of the solution are established under appropriate regularity assumptions. The proposed framework is validated using health insurance data from Asmari Insurance Company for the period 2022–2023. The numerical results demonstrate that the proposed approach provides stable and computationally efficient optimal coverage limits while effectively controlling portfolio risk, illustrating its potential as a practical decision-support tool for health insurance contract design.

Keywords

Coverage Limit Optimization
Health Insurance
Exponential Utility
Probabilistic Constraints
Portfolio Risk Management
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Journal of Mathematics and Modeling in Finance

Articles in Press, Accepted Manuscript
Available Online from 22 September 2026

  • Receive Date 11 May 2026
  • Revise Date 25 August 2026
  • Accept Date 12 September 2026

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