不完全半鞅市场中具有棘轮约束和收缩约束的消费效用最大化

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-01 DOI:10.1214/22-aap1918

Anastasiya Tanana

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引用次数: 1

摘要

本文利用对偶方法研究了一般不完全半鞅市场在棘轮约束和递减约束下的期望效用最大化问题。考虑了两个参数的优化:初始财富和消费过程的基本下界。为了说明问题和定义原域，我们将极大值运行的概念自然推广到任意非负可选过程，并研究了它的性质。优化的对偶域的特征是相对于在非负可选过程集上引入的排序的稳固性。利用我们对最优化问题所得到的抽象对偶结果，得到了完全市场情况下解的更详细的表征。

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Utility maximization with ratchet and drawdown constraints on consumption in incomplete semimartingale markets

In this paper, we study expected utility maximization under ratchet and drawdown constraints on consumption in a general incomplete semimartingale market using duality methods. The optimization is considered with respect to two parameters: the initial wealth and the essential lower bound on consumption process. In order to state the problem and define the primal domains, we introduce a natural extension of the notion of running maximum to arbitrary nonnegative optional processes and study its properties. The dual domains for optimization are characterized in terms of solidity with respect to an ordering that is introduced on the set of nonnegative optional processes. The abstract duality result we obtain for the optimization problem is used in order to derive a more detailed characterization of solutions in the complete market case.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.