Optimal Risk Transfer with Imperfect Hedging: A Framework for Insurers

Risk transfer mechanisms increasingly rely on instruments whose payoffs are imperfectly aligned with the underlying exposures they are intended to hedge.

This misalignment generates basis risk and complicates the evaluation of optimal coverage decisions for insurers. Understanding how insurers determine the appropriate level of coverage when hedging effectiveness is limited therefore represents a relevant problem in insurance risk management.

This work develops a stylized analytical framework to study the insurer’s optimal risk transfer decision in the presence of imperfect hedging.

The insurer faces a stochastic loss process and can transfer risk through an external instrument whose payoff is only partially correlated with the underlying exposure. The effectiveness of the hedge is therefore driven by the statistical relationship between the loss process and the hedging instrument.

The insurer’s decision problem is modeled as a trade-off between risk reduction and expected profitability. Risk mitigation is achieved by transferring part of the exposure, while expected profitability is constrained by an endogenous minimum profit requirement reflecting managerial preferences and business sustainability considerations.

Within this setting, the model characterizes the optimal level of coverage as a function of hedge effectiveness, pricing conditions, and the insurer’s tolerance for residual risk. The analysis highlights how imperfect hedging generates distinct coverage regimes and may lead insurers to adopt partial risk transfer even when hedging instruments are available.

The framework provides a simple analytical structure that helps interpret heterogeneous coverage choices observed in practice.