AI 中文总结
本文研究带跳跃信号的多资产投资组合效用最大化问题，通过半鞅表示与带跳跃BSDE刻画最优策略，证明解的存在唯一性并处理异质信号情形，给出高斯信号下的数值示例。
AI 中文摘要
本文研究在风险资产由多维布朗运动和独立齐次泊松随机测度驱动、策略可纳入跳跃信号的环境下的投资组合效用最大化问题。遵循一维情形下指数效用函数的方法[17]，我们首先将投资组合动态表示为半鞅过程，随后利用鞅最优性原理推导带跳跃的相应倒向随机微分方程（BSDE），通过其解刻画价值函数与最优策略；接着证明相关带跳跃BSDE解的存在性与唯一性，还针对投资者接收异质跳跃信号的特殊情形进行分析，最后针对对数效用情形，提供了高斯信号下的数值示例。
英文摘要
In this paper, we study portfolio utility maximization problem in a setting where the risky asset is driven by a multidimensional Brownian motion and an independent homogeneous Poisson random measure, and where strategies may incorporate jump signals. Following the same approach as in the one-dimensional case for the exponential utility function [17], we first represent the portfolio dynamics as semimartingale processes. We then use martingale optimality principle to derive the corresponding backward stochastic differential equation (BSDE) with jumps to characterize both value function and an optimal strategy in terms of its solution. We subsequently prove the existence and uniqueness of the solution to the related BSDE with jumps. We also address the idiosyncratic case i.e where the investor receive heterogeneous jump signals. Finally, we provide numerical illustrations with Gaussian signals for the logarithmic case.
