Hey judge: don’t let me down! A mechanism for optimal capital allocation to fund judicialization of claims in insurance companies

Litigation has become an increasingly relevant source of financial pressure for insurers, affecting both operational performance and long-term solvency. Although prior studies have shown that litigation raises operating costs and contributes to premium increases, the literature still lacks a technical, quantitatively grounded study to measure its joint impact on pricing and solvency capital. This study fills this gap by developing an analytical model, based on classical Risk Theory and the exponential premium principle, that derives the optimal sharing of litigation costs between policyholders and shareholders. The model incorporates litigation as an explicit operational cost, links it to the insurer’s adjustment coefficient and ruin probability, and derives closed-form solutions for (i) the optimal solvency capital that minimizes premiums, and (ii) the corresponding minimum premium that ensures technical and economic equilibrium. Using data from the Brazilian insurance market, we calibrate the model across multiple scenarios and quantify both the absolute and percentage effects of litigation on premium loadings and equity-capital requirements. The results show that litigation impacts premiums more strongly than solvency capital, although this effect varies across market segments. Larger insurers are able to absorb litigation costs more effectively through equity capital, partially shielding policyholders from premium increases, while smaller insurers tend to pass on a greater share of these costs via premiums. Beyond offering numerical evidence, this study introduces a formal actuarial criterion for the measurement of judicial provisions, addressing a longstanding gap in both regulation and accounting practice. The model provides insurers and regulators with an objective, replicable, and prudentially consistent tool for allocating litigation costs and managing related liabilities. By quantifying litigation’s dual impact on pricing and solvency, this study contributes to more efficient market functioning, enhanced transparency, and improved alignment between actuarial, accounting, and managerial perspectives.