Tax Loss Harvesting

Let E_t be the taxable earnings at time t.

Suppose an instrument was purchased at time t_0 at price P_{t_0}. If it is sold at time t_1 for price P_{t_1} the gain is P_{t_1} - P_{t_0}. The tax \tau(\Delta t).

Tax loss harvesting involves selling the instrument at time t_1 for price P_{t_1} < P_{t_0} and purchasing another instrument having price Q_{t_1}.