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假定股票价格服从连续时间的几何布朗运动,而交易只能在离散时点发生,交易存在固定-比例成本(佣金),投资者是风险厌恶的,论文研究了投资者的最优变现策略问题。首先,给出了变现策略的数学描述及投资者的目标函数。然后,用样条函数来刻画一个交易日内的相对变现折现率。接着,给出了价格冲击函数。最后,给出一个算例。研究结果表明,在不同的风险偏好情况下,无论天内流动性随时间变化的形状如何,股票的流动性越差,投资者越是尽早卖出手中的头寸;流动性越好,卖出的时间越往后推迟;投资者越是厌恶风险,投资者越是选择在股票市场收盘前尽可能多的卖出头寸。
Assuming that the stock price follows the geometric Brownian motion of continuous time and the transaction can only occur at discrete time points, the transaction has a fixed-proportional cost (commission) and the investor is risk-averse. The thesis studies the investor’s optimal realization strategy. First, the mathematical description of the realization strategy and the investor’s objective function are given. Then, use the spline function to characterize the relative realization discount rate in a trading day. Then, the price shock function is given. Finally, give an example. The results show that under different risk appetite, no matter the shape of liquidity changes with time, the stock liquidity is worse, the more investors sell their positions as soon as possible. The better the liquidity and the time to sell The later postponed; the more investors risk aversion, the more investors choose to sell as many positions as possible before the stock market closes.