Optimal control strategy of institutional investor's execution cost

摘要

Optimal control of multi-assets liquidation in view of volatility risk was studied. The analytical solution of optimal strategy was achieved with the calculus of variation. Numerical examples and graphical illustrations were also given. The conclusion shows that the optimal strategy is the linear combination of time's hyperbolic sine and hyperbolic cosine. The investor's attitude towards risk can influence the optimal strategy. In order to avoid the uncertainty of the execution cost, the investor with high risk aversion liquidates assets rapidly in the early period. The decrease of liquidation loss is at the cost of the increase of the volatility level.