Equilibrium strategies under model uncertainty in a shareholder–manager differential game for insurance firms

This paper studies the strategic interaction between shareholders and managers in an insurance company under model uncertainty using a two-player non-cooperative differential game. The firm’s surplus serves as the state variable, with the shareholder choosing dividend and capital-injection policies to maximise the expected discounted value of dividends net of financing costs, while the manager independently selects an excess-of-loss reinsurance strategy to maximise expected utility. To capture heterogeneous ambiguity attitudes, we examine three scenarios: (i) a benchmark case in which both parties fully trust the reference model; (ii) a setting where only the shareholder is ambiguity-averse; and (iii) a case where both agents face model uncertainty, potentially with different beliefs about surplus dynamics. The analysis characterises robust Nash equilibria across these settings and highlights how ambiguity aversion influences risk retention, dividend distribution, and capital support. Numerical results reveal nonlinear and asymmetric effects of managerial risk aversion and capital-injection costs, offering new insights into the role of heterogeneous beliefs in corporate governance and insurance risk management.