A stochastic optimal control strategy for partially observable nonlinear quasi Hamiltonian systems is proposed. The optimal control forces consist of two parts. The first part is determined by the conditions under whi...A stochastic optimal control strategy for partially observable nonlinear quasi Hamiltonian systems is proposed. The optimal control forces consist of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system. The response of the optimally controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation associated with the optimally controlled completely observable linear system and solving the Riccati equation for the estimated error of system states. An example is given to illustrate the procedure and effectiveness of the proposed control strategy.展开更多
Exercise-price policy is perhaps the central design issue regarding nontradable Executive Stock Options (ESO). In this paper, we give the value line of ESO, V(P), and the range of the incentive-maximizing exercise pri...Exercise-price policy is perhaps the central design issue regarding nontradable Executive Stock Options (ESO). In this paper, we give the value line of ESO, V(P), and the range of the incentive-maximizing exercise prices which is defined as the exercise prices that generate incentives, εn(P)/εP, within 1 percent of the maximum using the “certainty equivalence” approach, similar to that adopted by Richard Lambert et al.. Our results show that, holding constant the company's cost of making an option grant, incentives are maximized by setting exercise prices within a range that typically includes the grant-date market price.展开更多
基金Project supported by the National Natural Science Foundation ofChina (No. 10332030), the Special Fund for Doctor Programs inInstitutions of Higher Learning of China (No. 20020335092), andthe Zhejiang Provincial Natural Science Foundation (No. 101046),China
文摘A stochastic optimal control strategy for partially observable nonlinear quasi Hamiltonian systems is proposed. The optimal control forces consist of two parts. The first part is determined by the conditions under which the stochastic optimal control problem of a partially observable nonlinear system is converted into that of a completely observable linear system. The second part is determined by solving the dynamical programming equation derived by applying the stochastic averaging method and stochastic dynamical programming principle to the completely observable linear control system. The response of the optimally controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation associated with the optimally controlled completely observable linear system and solving the Riccati equation for the estimated error of system states. An example is given to illustrate the procedure and effectiveness of the proposed control strategy.
文摘Exercise-price policy is perhaps the central design issue regarding nontradable Executive Stock Options (ESO). In this paper, we give the value line of ESO, V(P), and the range of the incentive-maximizing exercise prices which is defined as the exercise prices that generate incentives, εn(P)/εP, within 1 percent of the maximum using the “certainty equivalence” approach, similar to that adopted by Richard Lambert et al.. Our results show that, holding constant the company's cost of making an option grant, incentives are maximized by setting exercise prices within a range that typically includes the grant-date market price.
