De Finetti’s control problem with a concave bound on the control rate

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Applied Probability Pub Date : 2024-01-25 DOI:10.1017/jpr.2023.87

Félix Locas, Jean-François Renaud

引用次数: 0

Abstract

We consider De Finetti’s control problem for absolutely continuous strategies with control rates bounded by a concave function and prove that a generalized mean-reverting strategy is optimal in a Brownian model. In order to solve this problem, we need to deal with a nonlinear Ornstein–Uhlenbeck process. Despite the level of generality of the bound imposed on the rate, an explicit expression for the value function is obtained up to the evaluation of two functions. This optimal control problem has, as special cases, those solved in Jeanblanc-Picqué and Shiryaev (1995) and Renaud and Simard (2021) when the control rate is bounded by a constant and a linear function, respectively.

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德菲内蒂控制问题与控制率的凹约束

我们考虑了控制率以凹函数为界的绝对连续策略的德菲内蒂控制问题，并证明在布朗模型中，广义均值回复策略是最优的。为了解决这个问题，我们需要处理一个非线性奥恩斯坦-乌伦贝克过程。尽管对速率施加的约束具有一定的普遍性，但在对两个函数进行评估之前，我们还是得到了价值函数的明确表达式。这一最优控制问题的特例包括 Jeanblanc-Picqué 和 Shiryaev (1995) 以及 Renaud 和 Simard (2021)分别在控制率受常数和线性函数约束时解决的问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Applied Probability 数学-统计学与概率论

CiteScore

1.50

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Applied Probability is the oldest journal devoted to the publication of research in the field of applied probability. It is an international journal published by the Applied Probability Trust, and it serves as a companion publication to the Advances in Applied Probability. Its wide audience includes leading researchers across the entire spectrum of applied probability, including biosciences applications, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used. A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.