LIN Yu, WU Weiping, WANG Zhenghong, JIN Chengneng
In optimal execution theory, risk-averse investors typically strive to strike a delicate balance between price impact and transaction execution risk when formulating trading decisions, with trading behavior substantially influenced by regulatory policies. Simultaneously, precise characterization of the actual limit order book (LOB) market is proved beneficial for investors in applying optimal execution theory to algorithmic trading practices. Leveraging these foundations, this paper examines the execution problems faced by investors with constant absolute risk aversion (CARA) utility preferences. The analysis is grounded in the general assumption of power-shaped stochastic market depth. Subsequently, we construct an optimal execution model grounded in this general assumption and the dynamics of the LOB market, incorporating considerations of trading risk and trading constraints. The least squares Monte Carlo (LSM) method is employed to derive the corresponding approximate trading strategy, accompanied by the provision of the theoretical upper bound for the approximation error. The numerical examples demonstrate that, within the framework of power-shaped stochastic market depth, the execution strategy for risk-averse investors exhibits a distinctive “L”-shaped characteristic. Simultaneously, the stochastic characteristics, shape profile of market depth, and trading constraints all exert significant influences on the execution strategies. Moreover, in terms of investment performance, the model presented in this paper effectively reduces execution risk and enhances the strategy's efficacy across various trading constraints. Furthermore, the trading constraints, the shape of the limit order book's market depth, and the speed at which the market rebounds also significantly impact both execution risk and the effectiveness of the strategy.
