Optimal compensation and investment affected by firm size and time-varying external factors

We investigate a continuous dynamic model associated with a firm size term and with an external factor term, which possesses the following peculiarities: the drift term is dominated by the principal’s investment strategy and the agent’s effort; the volatility term relies on the function \(\sqrt{G^2(t)+z_t}\) in which \(G(t)\ge 0\) is a continuously bounded function and is interpreted as external factors such as external variant risks, and \(z_t\) represents the firm size. The exact optimal contracts are obtained under full information. We find that the principal’s dividends in large firms are at lower risk since the flow of dividends increases with firm size. The optimal compensation scheme for the agent and investment plan for the principal are analyzed under specific assumptions. In extremely volatile environment with large G(t), the compensation for the agent would become overly large and the optimal investment is not achievable.