发表机构
UNIST; KAIST（蔚山科学技术院; 韩国科学技术院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究具有比例交易成本和随机交易机会的有限期限投资组合优化，允许非凹效用，通过求解半线性非局部HJB方程获得最优策略，数值显示非凹效用导致交易区间多重性和非标准交易顺序。
AI 中文摘要
我们研究了有限期限内的投资组合优化问题，该问题涉及比例交易成本，且交易机会在Cox过程的跳跃时刻到达。禁止借贷和卖空，而效用函数不必是凹的、递增的或可微的。可容许类别包括具有大于或等于一的渐近弹性的可微效用函数。相关的Hamilton--Jacobi--Bellman方程是半线性和非局部的，控制仅通过零阶项进入。我们证明了归一化方程具有唯一的有界解，该解在所有状态变量上连续，在时间和对数价格上是经典的。证明结合了压缩论证与内部Schauder估计，验证确定了值函数并产生最优马尔可夫反馈策略。使用非凹效用函数的数值例子表明，在固定时间和交易前财富下，存在与相同交易行为相关联的多个区间，偏离通常的买入--不交易--卖出顺序，以及最优交易后风险权重的突然切换。
英文摘要
We study finite-horizon portfolio optimization with proportional transaction costs and trading opportunities arriving at the jump times of a Cox process. Borrowing and short-selling are prohibited, while utility functions need not be concave, increasing, or differentiable. The admissible class includes differentiable utilities with asymptotic elasticity greater than or equal to one. The associated Hamilton--Jacobi--Bellman equation is semi-linear and nonlocal, with control entering only through a zeroth-order term. We show that the normalized equation admits a unique bounded solution that is continuous in all state variables and classical in time and log-price. The proof combines a contraction argument with interior Schauder estimates, and verification identifies the value function and yields an optimal Markovian feedback strategy. Numerical examples with non-concave utilities exhibit, at fixed time and pre-trade wealth, multiple intervals associated with the same trading action, departures from the usual buy--no-trade--sell ordering, and abrupt switches in the optimal post-trade risky weight.
Comments39 pages
