We consider a Heston local-stochastic volatility (HLSV) model to study the optimal investment, consumption, and work effort strategies for an executive with equity incentives and stochastic salary. The executive’s work behavior can affect the stock price of the company, and after retirement, he can choose whether to accept re-employment. Our goal is to maximize the expected discounted utility of consumption and terminal wealth and reduce the loss utility generated by work. In addition, we establish the Hamilton–Jacobi–Bellman (HJB) equation through the dynamic programming principle and solve complex nonlinear partial differential equations using a perturbation method to obtain asymptotic solutions for the optimal strategies and value function under the HLSV model. We also consider a general case in which the price process of risky asset follows the stochastic volatility (SV) model, which can be compared with the HLSV model. Finally, we provide a numerical example to illustrate the impact of some important parameters on the optimal strategies and value function.

我们考虑使用 Heston 局部随机波动率 (HLSV) 模型来研究具有股权激励和随机薪资的高管的最佳投资、消费和工作努力策略。高管的工作行为可以影响公司的股价，退休后可以选择是否接受再聘用。我们的目标是最大化消费和终端财富的预期贴现效用，并减少工作产生的损失效用。此外，我们通过动态规划原理建立Hamilton-Jacobi-Bellman（HJB）方程，并使用摄动方法求解复杂的非线性偏微分方程，以获得HLSV模型下最优策略和价值函数的渐近解。我们还考虑了一种一般情况，其中风险资产的价格过程遵循随机波动率（SV）模型，可以与 HLSV 模型进行比较。最后，我们提供了一个数值例子来说明一些重要参数对最优策略和价值函数的影响。