带交易成本的非凹效用最大化
Non-Concave Utility Maximization with Transaction Costs
AI总结：
本文研究带比例交易成本的非凹终端效用投资组合问题，通过渐近终端行为和不连续粘性解建立理论刻画，数值分析表明交易成本会改变投资者在风险资产上的最优多空头寸。
摘要：
本文研究了一个有限期投资组合选择问题，其中终端效用为非凹函数且存在比例交易成本，此时常用的终端价值凹化原理不再适用。我们通过两步程序建立了该问题的恰当理论刻画。首先，我们考察了价值函数的渐近终端行为，结果表明任何接近到期日的交易对效用仅提供边际贡献。其次，我们以不连续粘性解的形式建立了理论基础，并纳入了终端条件的恰当刻画。通过对多种类型效用函数的大量数值分析，我们发现，将交易成本引入非凹效用最大化问题后，与无摩擦情形相比，投资者持有更大的风险资产多头头寸可能是最优的，或者尽管风险溢价为正，持有风险资产的大量空头头寸也可能是最优的。
英文摘要：
This paper studies a finite-horizon portfolio selection problem with non-concave terminal utility and proportional transaction costs, in which the commonly used concavification principle for terminal value is no longer applicable. We establish a proper theoretical characterization of this problem via a two-step procedure. First, we examine the asymptotic terminal behavior of the value function, which implies that any transaction close to maturity only provides a marginal contribution to the utility. Second, we establish the theoretical foundation in terms of the discontinuous viscosity solution, incorporating the proper characterization of the terminal condition. Via extensive numerical analyses involving several types of utility functions, we find that the introduction of transaction costs into non-concave utility maximization problems can make it optimal for investors to hold on to a larger long position in the risky asset compared to the frictionless case, or hold on to a large short position in the risky asset despite a positive risk premium.
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