Optimal pricing barriers in a regulated market using reflected diffusion processes
研究了一类一维反射随机微分方程，用于确定受监管金融市场中的最优定价边界，考虑了长期平均成本和可变贴现成本，并给出了数值例子。
We consider a class of one-dimensional (1D) reflected stochastic differential equations (SDEs). Such reflected SDE models arise as the key approximating processes in a regulated financial market system, and our main goal is to determine the set of optimal pricing barriers. We consider the running cost associated with the deviation of the process from the desired target level, and also the control cost from the interventions in an effort to keep the process inside the boundaries. Both a long-time average (ergodic) cost criterion and an infinite horizon discount cost criterion, where the discount factor is allowed to vary from one period to another, are studied, with numerical examples illustrating our main results.