几何布朗运动市场中的最优变现策略研究

Researchs on Optimal Liquidation Strategies in Geometric Brown Markets

利用相对价格冲击函数的Box-Cox变换和存在比例交易费用的线性函数,研究了非瓦尔拉斯均衡金融市场上风险资产的价格变现策略,当资产价格变化服从几何布朗运动时,资产变现时间内生情形下投资者最优变现策略问题可以转化为具有随机跳出时间的随机最优控制,通过对带有广义狄利克雷边界条件的贝尔曼方程的粘性求解,可以实现最优变现策略。

The optimal liquidation strategy are studied in a non-Walrasian market ,in which the price of risk assets is the solution of a Geometry-Brown stochastic differential equation ,and the relative price-impact function is a linear function of Box-Cox transformation and there exist proportion transaction fee .The liquidation problem with endogenous liquidation time is a optimal stochastic control equipped with an stochastic exit time .According to the viscosity solution theory,the optimal liquidation is obtained by discussing a Hamihon-Jacobi-Bellman equation with generalized Dirichlet boundary conditions.