带比例交易成本与对数Lévy资产价格的长期风险敏感投资组合优化
Long-run risk-sensitive portfolio optimisation with proportional transaction costs and log Lévy asset prices
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中文总结 AI 辅助
针对对数Lévy资产价格且仅可在随机投资机会再平衡的连续时间市场，研究带比例交易成本的长期风险敏感投资组合优化，求解遍历Bellman方程并验证相关渐近性与收敛性，数值示例佐证结果。
中文摘要 AI 辅助
我们研究连续时间市场中的长期风险敏感投资组合问题，该市场具备比例交易成本，资产对数价格由Lévy过程给出，且仅能在随机投资机会时刻进行再平衡。借助Schauder不动点论证，我们在无任何混合假设的情况下求解遍历Bellman方程；在额外的全支撑与增长条件下，Bellman方程的解是唯一的，且具有唯一的连续最大化器。我们还证明了风险厌恶趋近于风险中性（Kelly）问题的渐近性，以及随机干预时刻的二元时间网格近似的收敛性，数值示例验证了所得结果。
英文摘要
We study a long-run risk-sensitive portfolio problem with proportional transaction costs in a continuous-time market whose log-prices are given as a Lévy process, and rebalancing is possible only at random moments of investment opportunities. Using a Schauder fixed-point argument, we solve the ergodic Bellman equation without any mixing assumptions. Under additional full-support and growth conditions, the solution to the Bellman equation is unique, with the unique continuous maximiser. We also prove vanishing risk-aversion asymptotics towards the risk-neutral (Kelly) problem and convergence of a dyadic-time-grid approximation of the random intervention moments. Numerical examples illustrate the results.
