constrained premium optimization

This study addresses the profit optimization problem faced by insurers under solvency regulation (e.g., Solvency II, Swiss Solvency Test) and risk appetite constraints. We develop a risk-appetite-driven, multi-stage asset allocation optimization framework that integrates mathematical programming with dynamic solvency modeling. Methodologically, we systematically derive and quantify the annual opportunity cost induced by regulatory compliance constraints—a novel contribution. Our key contributions are threefold: (1) a unified, regulator-agnostic optimization paradigm adaptable across diverse solvency regimes; (2) economic profit maximization subject to a given risk tolerance threshold; and (3) empirical quantification of the true economic cost of regulatory compliance, providing actionable, evidence-based insights for strategic capital allocation and regulatory dialogue in life, non-life, and reinsurance firms. The framework bridges theoretical rigor with practical applicability, enabling insurers to balance prudential requirements with value creation objectives.

This paper addresses the optimal asset allocation problem for (re)insurers subject to regulatory Conditional Value-at-Risk (CVaR) constraints. To overcome the computational intractability of exact CVaR-constrained optimization, we propose a sample-average approximation (SAA)-based stochastic optimization framework. First, we establish the strong consistency of the SAA estimator under minimal distributional assumptions, derive an explicit convergence rate, and provide sufficient conditions for uniqueness of the optimal solution. The framework thus bridges theoretical rigor with computational tractability, yielding a provably convergent and implementable risk-compliant investment strategy. It enhances capital efficiency and portfolio robustness while ensuring regulatory compliance and prudent risk management.

This study addresses the issue of suboptimal, non-comonotonic risk sharing that arises when regulatory or contractual constraints undermine incentives for risk-averse agents. The paper introduces “quantile-convex order robustness” as a sufficient condition on the feasible set under which a comonotonic improvement exists for all preferences consistent with the convex order, thereby restoring the comonotonicity between Pareto-optimal allocations and aggregate losses. This condition encompasses common risk management constraints—such as value-at-risk (VaR) caps and individual deductibles—and is validated within the mean-variance framework. The result provides a unified and tractable theoretical foundation for constrained risk-sharing problems.

Financial institutions face persistent challenges in hedging interest rate risk for long-term asset–liability mismatches. Method: This paper proposes a bond portfolio construction framework grounded in ambiguity-averse preferences, systematically integrating such preferences into asset–liability management (ALM). The approach accommodates arbitrary liability structures, investment constraints, and interest rate shocks, extending classical immunization theory. Uncertainty is modeled via fuzzy sets; portfolio optimization employs generalized least squares under an arbitrage-free term structure model, inducing implicit regularization that curbs leverage and enhances out-of-sample robustness. Contribution/Results: Numerical experiments and empirical yield curve analyses demonstrate that the proposed method achieves superior hedging accuracy, computational efficiency, and robustness across multiple scenarios compared to existing approaches. The model is transparent, interpretable, and readily implementable in practice.

Traditional insurance pricing often neglects policyholders’ price sensitivity, hindering revenue optimization. This work formulates pricing as a sequential decision-making problem and introduces an optimization framework that integrates off-policy evaluation with stochastic control. The proposed approach employs a kernelized inverse propensity score estimator that leverages the local structure of the action space to reduce variance and combines an interpretable Lasso model with neural networks for policy parameterization. Experimental results in a synthetic travel insurance environment demonstrate that the method significantly outperforms existing techniques, achieving higher pricing revenue while preserving policy interpretability.

This work addresses the challenge of accurately identifying optimal policies and active constraints when both are unknown. It proposes a unified simulation-grid-based dual framework that integrates Fenchel duality, Doob martingale compensation, complementary slackness, and occupancy-measure weighting. By decomposing residuals via conditional budget identities and leveraging Bellman curvature, the method constructs a tight policy region without requiring a reference solution. It simultaneously estimates policy error, certifies active constraint facets, and provides joint verification of value bounds and policy distance. Empirical results demonstrate its ability to achieve full coverage in auditing external policy errors, deliver zero false positives in active facet detection, maintain tightness in 50-dimensional asset stress tests, and reveal that dual-learning accuracy becomes the performance bottleneck in high dimensions.

This study addresses the design of optimal insurance contracts by a monopolist facing dual private information: policyholders’ risk types and their risk aversion levels, under asymmetric information. Within a Stackelberg framework and adopting the expected-value premium principle, the authors formulate a mean-variance utility maximization problem subject to incentive compatibility and individual rationality constraints. Leveraging mechanism design theory, calculus of variations, and ordinary differential equations (ODEs), they derive the optimal contract structure. The key contributions include the novel finding that when risk aversion depends on risk type, the optimal contract takes the form of excess-of-loss coverage; the derivation of an ODE characterizing the risk-loading component, along with a proof of its existence and uniqueness; and the discovery of a nonlinear pricing pattern wherein higher-risk individuals face lower risk-loading premiums. Numerical simulations further illustrate how heterogeneity in risk distributions shapes the optimal contract design.

This work addresses the challenge of unifying the modeling of stochastic objectives such as risk, bias, regret, and error by proposing an optimization framework grounded in a generalized “risk quadrangle.” By incorporating advanced risk measures like superquantiles and expectiles, and by developing a “sub-regularity” axiom system that relaxes conventional regularity assumptions, the approach overcomes limitations of classical theory and enhances model flexibility. Leveraging duality analysis, generalized stochastic divergences, and robust optimization techniques, the framework demonstrates superior performance in portfolio optimization, regression, and classification tasks. The study highlights the central role of duality in risk-sensitive decision-making and significantly broadens the applicability of risk modeling in machine learning, finance, and related domains.