全动态风险度量：水平风险、时间一致性以及与 BSDE 和 BSVIE 的关系

IF 1.4 4区经济学 Q3 BUSINESS, FINANCE

SIAM Journal on Financial Mathematics Pub Date : 2024-05-21 DOI:10.1137/23m1546804

Giulia Di Nunno, Emanuela Rosazza Gianin

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引用次数: 0

摘要

SIAM 金融数学期刊》第 15 卷第 2 期第 399-435 页，2024 年 6 月。摘要.在一个动态框架中，我们发现了一个新的概念，它与用不符合头寸实际时间跨度的方法来评估金融风险敞口的风险有关。这将被称为时间跨度风险。我们明确指出，动态风险度量受地平线风险的影响，因此我们建议使用完全动态版本。为了量化地平线风险，我们引入了 h-longevity 作为指标。我们将这些概念与风险度量的其他属性一起研究，如归一化、限制属性和时间一致性的不同表述。我们还考虑了由后向随机微分方程 (BSDE)、后向随机伏特拉积分方程 (BSVIE) 及其族生成的全动态风险度量的这些概念。在这项研究中，我们为 BSVIEs 提供了新的结果，如反向比较定理和相关风险度量的对偶表示。

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Fully Dynamic Risk Measures: Horizon Risk, Time-Consistency, and Relations with BSDEs and BSVIEs

SIAM Journal on Financial Mathematics, Volume 15, Issue 2, Page 399-435, June 2024.
Abstract.In a dynamic framework, we identify a new concept associated with the risk of assessing the financial exposure by a measure that is not adequate to the actual time horizon of the position. This will be called horizon risk. We clarify that dynamic risk measures are subject to horizon risk, so we propose to use the fully dynamic version. To quantify horizon risk, we introduce h-longevity as an indicator. We investigate these notions together with other properties of risk measures, such as normalization, restriction property, and different formulations of time-consistency. We also consider these concepts for fully dynamic risk measures generated by backward stochastic differential equations (BSDEs), backward stochastic Volterra integral equations (BSVIEs), and families of these. Within this study, we provide new results for BSVIEs, such as a converse comparison theorem and the dual representation of the associated risk measures.

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来源期刊

SIAM Journal on Financial Mathematics MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

2.30

自引率

10.00%

发文量

期刊介绍： SIAM Journal on Financial Mathematics (SIFIN) addresses theoretical developments in financial mathematics as well as breakthroughs in the computational challenges they encompass. The journal provides a common platform for scholars interested in the mathematical theory of finance as well as practitioners interested in rigorous treatments of the scientific computational issues related to implementation. On the theoretical side, the journal publishes articles with demonstrable mathematical developments motivated by models of modern finance. On the computational side, it publishes articles introducing new methods and algorithms representing significant (as opposed to incremental) improvements on the existing state of affairs of modern numerical implementations of applied financial mathematics.