Problems Of Optimal Execution Under Jump-diffusion Processes

After years of development,theoretical research and practice the execution of the order have made great achievements,but the general market impact model does not consider the execution risk and the optimal strategy is actually a static strategy.Both in theory and in practice,there are some deficiencies.Cheng et al.(Quantitative Finance)extend the classical price impact model of Almgren and Chriss to incorporate the uncertainty of order fills and use the new model including execution risk to solve some problems with uncertain order fills.We further extend the model that the dynamics of position are driven by a Brownian motion and a Poisson random measure.We consider the expectation of P&L(Profit and Loss)as the goal and obtain the optimal execution strategies under certain conditions by solving the stochastic control problem.The Momentum trading strategy in the financial market has become more widely used.We have screened out 207 mutual funds in different markets,which well reflect the investor's choice of momentum trading strategy and the shifts of contrarian strategy.According to data experiments,we know that different strategic choices reflect different impacts and we evaluate the performance of these strategic choices during the financial crisis.The experimental results show that the excellent fund managers usually choose the momentum trading strategy before the financial crisis and no longer use it in the midst of the financial crisis.Then they choose the contrarian strategy.This paper not only provides the optimal choice of strategy portfolio,but also provides the best method of investment strategy.