On Models For La-ES And Optimal Liquidation Strategies

Liquidity risk is one of the three core financial risk described by Basel AccordⅠand Basel AccordⅡand attracts people's attentions more and more. Academic research on liquidity risk has become the focus of study.Dissertation investigated the problems of optimal liquidation strategy and Liquidity–Adjusted Expected Shortfall (La-ES) belonging to the coherent risk measure. First of all, from the aspect of bid-ask spread the computation method of La-ES was discussed, and then the computation method of La-ES was presented when both continuous return ratio of medium price and relative semi-price followed normal distribution; furthermore, La-ES was proposed by utilizing MGARCH; for describing inter-relationship of multi-variable better, it was necessary to introduce method of Copula for modeling, so the method and diagram of La-ES were obtained. Secondly, the dissertation studied also La-ES by the supply curve. There were two situations as follows: as the supply curve was linear, the analytical solution was presented by implementing; similarly, as the supply curve was exponent function, semi-analytical solution was also obtained by maximum principle, and the method and formula for computing La-ES by Monte Carlo Simulation were given. Thirdly, the problems of institution investor'optimal liquidation strategy and optimal liquidation time were investigated with the conditions that the price of risky asset followed arithmetic Brown motion and liquidation velocity was limited. The problems involved the following scenes: price impact function was linear expression of liquidation velocity which was boundary closed set with an isolated point; price impact function was stochastic; price impact function was nonlinear. Finally, the dissertation discussed the problem of optimal liquidation strategy with price following geometry Brown motion: for the discrete liquidation time, VaR and ES of the total liquidation revenue were given under the known liquidation strategy, that is, La-VaR and La-ES; for continuous liquidation time, the problem of institution investor'optimal liquidation strategy was presented as a stochastic optimal control model, and synchronously, partial differential equation and its analytical solution were obtained by using dynamic programming method.In conclusion , from the aspect of liquidity this dissertation introduce the model of La-ES, takes account of the effect on measuring risk suffering from market situation, position size and the risk preference of investors, and investigates deeply risk management in financial market in theory. Such provides the referenced models and methods for the participator and supervisor in financial market. There will be positive theoretical worth and practical significance.