主要研究了``安全第一"原则下的连续时间随机过程的投资组合问题, 所考察的模型是带有布朗运动和跳跃扩散的随机过程. 推导出了相应的哈密顿雅克比贝尔曼方程. 当不存在无风险资产时, 得出了最优投资策略的闭环解. 同样讨论了存在无风险资产投资时的最优投资策略. 最后给出了一个实例加以说明此模型和方法的有效性和可行性.

This paper studies the portfolio problem of continuous-time stochastic processes under safety-first criterion, where the considered mathematical model is governed by the Brown motion and jump-diffusion process. The corresponding Hamilton-Jacobi-Bellman (HJB) equation of the problem is derived. The closed-form solutions of optimal strategies are presented when there is no riskless asset. Moreover, the optimal strategies of problem are also discussed while there is one riskless asset. Finally, a numerical example is given to illustrate the efficiency and feasibility of the constructed models and developed methods.