Mathematical model of optimal payouts under non-linear demand curve

In this study, a mathematical model that shows the optimal payout policy is developed. The model is new and unique in the sense that not only continuous-time framework is used, but also both partial differential equation and real-option approach are utilized in the derivation of optimal payouts for the first time. In the model building, non-linear demand curve for dividend payouts in the competitive capital markets is assumed. From the sensitivity analysis using traditional comparative static analysis, some useful managerial implications which are consistent with famous previous studies are derived under realistic conditions. All results in this study, however, are valid under the assumption that the opportunity costs follow geometric Brownian motion, which is widely used in economic science and finance literature.