We consider a multistep portfolio optimization problem. At every time step, capital can be invested either in a risk-free asset with fixed income or in a risky asset with a random return with a finite density. The optimality criterion is the probability of reaching or exceeding the investor’s capital at the terminal time moment at a certain predetermined level. Based on the use of piecewise constant control, we propose a positional control that surpasses previously known universal controls, which are used in portfolio optimization problems, in terms of the value of the probabilistic criterion on a wide set of examples.

中文翻译：

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具有概率准则的多步资产组合优化问题中位置控制的构造

我们考虑一个多步骤的投资组合优化问题。在每个时间步长，资本都可以投资于具有固定收益的无风险资产，也可以投资于具有有限密度的随机收益的风险资产。最优标准是在最终时刻达到或超过某个预定水平的投资者资本的可能性。基于分段常数控制的使用，我们提出了一种位置控制，其在许多示例中的概率准则的价值方面，超过了先前已知的用于投资组合优化问题的通用控制。