论文标题
内源性定价下的效用最大化
Utility maximization under endogenous pricing
论文作者
论文摘要
我们研究了一个大型投资者的预期公用事业最大化问题，他被允许在不完整的金融市场上对可交易资产进行交易，并具有内在的永久性市场影响。假定资产价格遵循市场中引用的非线性价格曲线，作为代表性流动性供应商的效用漠不关心曲线。我们表明，可以通过耦合前回向随机微分方程（FBSDE）的系统充分表征最佳性，该方程（FBSDE）对应于非线性的后向随机偏微分方程（BSPDE）。我们显示了在代表做市商的驾驶员功能至少二次增长或大型投资者的效用函数的情况下，解决最佳投资问题和FBSDE的解决方案的存在。此外，我们得出了BSPDE溶液的存在的平滑度。当市场完成或实用程序功能指数级时，提供了示例。
We study the expected utility maximization problem of a large investor who is allowed to make transactions on tradable assets in an incomplete financial market with endogenous permanent market impacts. The asset prices are assumed to follow a nonlinear price curve quoted in the market as the utility indifference curve of a representative liquidity supplier. We show that optimality can be fully characterized via a system of coupled forward-backward stochastic differential equations (FBSDEs) which corresponds to a non-linear backward stochastic partial differential equation (BSPDE). We show existence of solutions to the optimal investment problem and the FBSDEs in the case where the driver function of the representative market maker grows at least quadratically or the utility function of the large investor falls faster than quadratically or is exponential. Furthermore, we derive smoothness results for the existence of solutions of BSPDEs. Examples are provided when the market is complete or the utility function is exponential.
