Research On Liquidation Problem Of Capital Asset

Liquidity is an important factor in market pricing. In the area of investment, if the market liquidity is low, the investors have to endure heavy losses in the period of liquidtation. So an optimal liquidation strategy is essential to investment decisions. From 1998, Bertimas, Lo, Almgren, Chriss, Hisata and Yamai began to investigate the liquidation problem in a thin market. However, they always discuss static decion based on equilibrium theory.According to different understanding of the market information by the investors, our work can be divided to two following parts.First, if the market foreground is not clear, we can assume that the market price follows a random walk. Present literures proved that under such conditions, renew of parameters can cause few gains. So investors have to apply static decisions. In this area, we complete two jobs: (1) we investigate a liquidation strategy combined with a endougenous total liquidation time. A dynamic programming method is applied to obtain an analytic solution, and we also map it to a simple sequence. It is proved that the optimal liquidation time is infinity. We get a suboptimal solution in the term of a given error. (2) the delay time of a liquidation is also correlative with the liquidation quantity, which is neglected by present literures. We set the trade interval as the current delay time, and prove that the optimal execution strategy is close to a case of constant liquidation speed.Second, we reconsider the method of equilibrium theory, and invstigate the application of mathematical model in the research of finance in detail. We find that analysis of the liquidation problem is few in present literures. They build models on assumptions instead of understanding of the problem. By analyzing the characters of market trades we find that liquidation decisions is dynamic decisions in nature. Investors can choose different decision modes according to forecasting modes. Based on these understanding, we establish a common framework of liquidation problem. By space mapping principles, we confirm the relationship between the price curve and the optimal strategy. In the case of simple forecast price curve, we find out the optimal strategy and relative properties under maximum-maximum principle, decision principle. Finally, we analyse the sensitivity of parameters in optimal strategy and optimal total gain. And the renew model of information in the simple case is also given.