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Infinite-mean models in risk management: Discussions and recent advances 风险管理中的无穷均值模型:讨论与最新进展
arXiv - QuantFin - Risk Management Pub Date : 2024-08-16 DOI: arxiv-2408.08678
Yuyu Chen, Ruodu Wang
{"title":"Infinite-mean models in risk management: Discussions and recent advances","authors":"Yuyu Chen, Ruodu Wang","doi":"arxiv-2408.08678","DOIUrl":"https://doi.org/arxiv-2408.08678","url":null,"abstract":"In statistical analysis, many classic results require the assumption that\u0000models have finite mean or variance, including the most standard versions of\u0000the laws of large numbers and the central limit theorems. Such an assumption\u0000may not be completely innocent, and it may fail for datasets with heavy tails\u0000(e.g., catastrophic losses), relevant to financial risk management. In this\u0000paper, we discuss the importance of infinite-mean models in economics, finance,\u0000and related fields, with recent results and examples. We emphasize that many\u0000results or intuitions that hold for finite-mean models turn out to fail or even\u0000flip for infinite-mean models. Due to the breakdown of standard thinking for\u0000infinite-mean models, we argue that if the possibility of using infinite-mean\u0000models cannot be excluded, great caution should be taken when applying classic\u0000methods that are usually designed for finite-mean cases in finance and\u0000insurance.","PeriodicalId":501128,"journal":{"name":"arXiv - QuantFin - Risk Management","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142191323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Systemic values-at-risk and their sample-average approximations 系统风险值及其样本平均近似值
arXiv - QuantFin - Risk Management Pub Date : 2024-08-16 DOI: arxiv-2408.08511
Wissam AlAli, Çağın Ararat
{"title":"Systemic values-at-risk and their sample-average approximations","authors":"Wissam AlAli, Çağın Ararat","doi":"arxiv-2408.08511","DOIUrl":"https://doi.org/arxiv-2408.08511","url":null,"abstract":"This paper investigates the convergence properties of sample-average\u0000approximations (SAA) for set-valued systemic risk measures. We assume that the\u0000systemic risk measure is defined using a general aggregation function with some\u0000continuity properties and value-at-risk applied as a monetary risk measure. We\u0000focus on the theoretical convergence of its SAA under Wijsman and Hausdorff\u0000topologies for closed sets. After building the general theory, we provide an\u0000in-depth study of an important special case where the aggregation function is\u0000defined based on the Eisenberg-Noe network model. In this case, we provide\u0000mixed-integer programming formulations for calculating the SAA sets via their\u0000weighted-sum and norm-minimizing scalarizations. To demonstrate the\u0000applicability of our findings, we conduct a comprehensive sensitivity analysis\u0000by generating a financial network based on the preferential attachment model\u0000and modeling the economic disruptions via a Pareto distribution.","PeriodicalId":501128,"journal":{"name":"arXiv - QuantFin - Risk Management","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142191329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Concentration Risk Indicator: Raising the Bar for Financial Stability and Portfolio Performance Measurement 集中风险指标:提高金融稳定性和投资组合绩效衡量标准
arXiv - QuantFin - Risk Management Pub Date : 2024-08-14 DOI: arxiv-2408.07271
Ravi Kashyap
{"title":"The Concentration Risk Indicator: Raising the Bar for Financial Stability and Portfolio Performance Measurement","authors":"Ravi Kashyap","doi":"arxiv-2408.07271","DOIUrl":"https://doi.org/arxiv-2408.07271","url":null,"abstract":"We have developed a novel risk management measure called the concentration\u0000risk indicator (CRI). The CRI has been created to address drawbacks with\u0000prevailing methodologies and to supplement existing methods. Modified and\u0000adapted from the Herfindahl-Hirschman (HH) index, the CRI can give a single\u0000numeric score that can be helpful to evaluate the extent of risks that arise\u0000from holding concentrated portfolios. We discuss how the CRI can become an\u0000indicator of financial stability at any desired aggregation unit: regional,\u0000national or international level. We show how the CRI can be easily applied to\u0000insurance risk and to any product portfolio mix. The CRI is particularly\u0000applicable to the current facet of the decentralized terrain, wherein the\u0000majority of the wealth is restricted to a small number of tokens. We calculate\u0000and report the CRI -- along with other risk metrics -- for individual assets\u0000and portfolios of crypto assets using a daily data sample from January 01, 2019\u0000until August 10, 2022. The CRI is an example of developing metrics that can\u0000useful for sending concise yet powerful messages to the relevant audience. This\u0000tactic -- which can be described as marketing the benefits of any product or\u0000service by using concepts from multiple disciplines -- of creating new metrics\u0000goes further beyond the use of metrics to evaluate marketing efficacy. The\u0000simplicity of our metric -- and the intuitive explanations we have provided for\u0000the CRI -- makes it straightforward to properly articulate a strong -- clear\u0000and positive -- signal as part of marketing campaigns. The development -- and\u0000implementation -- of new risk management metrics will have greater impact when\u0000a wider rigorous risk management process has been established. We discuss\u0000several topics related to bringing about more improved risk management across\u0000all types of institutions and assets.","PeriodicalId":501128,"journal":{"name":"arXiv - QuantFin - Risk Management","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142191325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Reinsurance with neural networks 神经网络再保险
arXiv - QuantFin - Risk Management Pub Date : 2024-08-12 DOI: arxiv-2408.06168
Aleksandar Arandjelović, Julia Eisenberg
{"title":"Reinsurance with neural networks","authors":"Aleksandar Arandjelović, Julia Eisenberg","doi":"arxiv-2408.06168","DOIUrl":"https://doi.org/arxiv-2408.06168","url":null,"abstract":"We consider an insurance company which faces financial risk in the form of\u0000insurance claims and market-dependent surplus fluctuations. The company aims to\u0000simultaneously control its terminal wealth (e.g. at the end of an accounting\u0000period) and the ruin probability in a finite time interval by purchasing\u0000reinsurance. The target functional is given by the expected utility of terminal\u0000wealth perturbed by a modified Gerber-Shiu penalty function. We solve the\u0000problem of finding the optimal reinsurance strategy and the corresponding\u0000maximal target functional via neural networks. The procedure is illustrated by\u0000a numerical example, where the surplus process is given by a Cram'er-Lundberg\u0000model perturbed by a mean-reverting Ornstein-Uhlenbeck process.","PeriodicalId":501128,"journal":{"name":"arXiv - QuantFin - Risk Management","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142191327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Adaptive Multilevel Stochastic Approximation of the Value-at-Risk 风险价值的自适应多级随机近似值
arXiv - QuantFin - Risk Management Pub Date : 2024-08-12 DOI: arxiv-2408.06531
Stéphane Crépey, Noufel Frikha, Azar Louzi, Jonathan Spence
{"title":"Adaptive Multilevel Stochastic Approximation of the Value-at-Risk","authors":"Stéphane Crépey, Noufel Frikha, Azar Louzi, Jonathan Spence","doi":"arxiv-2408.06531","DOIUrl":"https://doi.org/arxiv-2408.06531","url":null,"abstract":"Cr'epey, Frikha, and Louzi (2023) introduced a multilevel stochastic\u0000approximation scheme to compute the value-at-risk of a financial loss that is\u0000only simulatable by Monte Carlo. The optimal complexity of the scheme is in\u0000$O({varepsilon}^{-5/2})$, ${varepsilon} > 0$ being a prescribed accuracy,\u0000which is suboptimal when compared to the canonical multilevel Monte Carlo\u0000performance. This suboptimality stems from the discontinuity of the Heaviside\u0000function involved in the biased stochastic gradient that is recursively\u0000evaluated to derive the value-at-risk. To mitigate this issue, this paper\u0000proposes and analyzes a multilevel stochastic approximation algorithm that\u0000adaptively selects the number of inner samples at each level, and proves that\u0000its optimal complexity is in $O({varepsilon}^{-2}|ln {varepsilon}|^{5/2})$.\u0000Our theoretical analysis is exemplified through numerical experiments.","PeriodicalId":501128,"journal":{"name":"arXiv - QuantFin - Risk Management","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142191326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Impact of Climate transition on Credit portfolio's loss with stochastic collateral 气候转型对随机抵押品信贷组合损失的影响
arXiv - QuantFin - Risk Management Pub Date : 2024-08-12 DOI: arxiv-2408.13266
Lionel Sopgoui
{"title":"Impact of Climate transition on Credit portfolio's loss with stochastic collateral","authors":"Lionel Sopgoui","doi":"arxiv-2408.13266","DOIUrl":"https://doi.org/arxiv-2408.13266","url":null,"abstract":"We propose models to quantify the distortion the credit portfolio (expected\u0000and unexpected) losses, when the obligor companies as well as their guarantees\u0000belong to an economy subject to the climate transition. The economy's\u0000productivity is modeled as a multidimensional Ornstein-Uhlenbeck (O.-U.)\u0000process while the climate transition is represented by a continuous\u0000deterministic carbon price process. We define each loan's loss at default as\u0000the difference between Exposure at Default (EAD) and the liquidated collateral,\u0000which will help us to define the Loss Given Default (LGD). We consider two\u0000types of collateral: financial asset (such as invoices, cash, or investments)\u0000or physical asset (such as real estate, business equipment, or inventory). For\u0000financial assets, we model them by the continuous time version of the\u0000discounted cash flows methodology, where the cash flows SDE is driven by the\u0000instantaneous output growth, the instantaneous growth of a carbon price\u0000function, and an arithmetic Brownian motion. For physical assets, we focus on\u0000property in the housing market. We define, as Sopgoui (2024), their value as\u0000the difference between the price of an equivalent efficient building following\u0000an exponential O.-U. as well as the actualized renovation costs and the\u0000actualized sum of the future additional energy costs due to the inefficiency of\u0000the building, before an optimal renovation date which depends on the carbon\u0000price process. Finally, we obtain how the loss' risk measures of a credit\u0000portfolio are skewed in the context of climate transition through carbon price\u0000and/or energy performance of buildings when both the obligors and their\u0000guarantees are affected. This work provides a methodology to calculate the\u0000(statistics of the) loss of a portfolio of secured loans, starting from a given\u0000climate transition scenario described by a carbon price.","PeriodicalId":501128,"journal":{"name":"arXiv - QuantFin - Risk Management","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142191328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Risk sharing with Lambda value at risk under heterogeneous beliefs 在异质信念条件下利用 Lambda 风险值分担风险
arXiv - QuantFin - Risk Management Pub Date : 2024-08-06 DOI: arxiv-2408.03147
Peng Liu, Andreas Tsanakas, Yunran Wei
{"title":"Risk sharing with Lambda value at risk under heterogeneous beliefs","authors":"Peng Liu, Andreas Tsanakas, Yunran Wei","doi":"arxiv-2408.03147","DOIUrl":"https://doi.org/arxiv-2408.03147","url":null,"abstract":"In this paper, we study the risk sharing problem among multiple agents using\u0000Lambda value at risk as their preferences under heterogenous beliefs, where the\u0000beliefs are represented by several probability measures. We obtain\u0000semi-explicit formulas for the inf-convolution of multiple Lambda value at risk\u0000under heterogenous beliefs and the explicit forms of the corresponding optimal\u0000allocations. To show the interplay among the beliefs, we consider three cases:\u0000homogeneous beliefs, conditional beliefs and absolutely continuous beliefs. For\u0000those cases, we find more explicit expressions for the inf-convolution, showing\u0000the influence of the relation of the beliefs on the inf-convolution. Moreover,\u0000we consider the inf-convolution of one Lambda value at risk and a general risk\u0000measure, including expected utility, distortion risk measures and Lambda value\u0000at risk as special cases, with different beliefs. The expression of the\u0000inf-convolution and the form of the optimal allocation are obtained. Finally,\u0000we discuss the risk sharing for another definition of Lambda value at risk.","PeriodicalId":501128,"journal":{"name":"arXiv - QuantFin - Risk Management","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141969072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An Integrated Approach to Importance Sampling and Machine Learning for Efficient Monte Carlo Estimation of Distortion Risk Measures in Black Box Models 有效蒙特卡罗估计黑盒模型失真风险度量的重要度采样和机器学习综合方法
arXiv - QuantFin - Risk Management Pub Date : 2024-08-05 DOI: arxiv-2408.02401
Sören Bettels, Stefan Weber
{"title":"An Integrated Approach to Importance Sampling and Machine Learning for Efficient Monte Carlo Estimation of Distortion Risk Measures in Black Box Models","authors":"Sören Bettels, Stefan Weber","doi":"arxiv-2408.02401","DOIUrl":"https://doi.org/arxiv-2408.02401","url":null,"abstract":"Distortion risk measures play a critical role in quantifying risks associated\u0000with uncertain outcomes. Accurately estimating these risk measures in the\u0000context of computationally expensive simulation models that lack analytical\u0000tractability is fundamental to effective risk management and decision making.\u0000In this paper, we propose an efficient important sampling method for distortion\u0000risk measures in such models that reduces the computational cost through\u0000machine learning. We demonstrate the applicability and efficiency of the Monte\u0000Carlo method in numerical experiments on various distortion risk measures and\u0000models.","PeriodicalId":501128,"journal":{"name":"arXiv - QuantFin - Risk Management","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Climate-Driven Doubling of Maize Loss Probability in U.S. Crop Insurance: Spatiotemporal Prediction and Possible Policy Responses 气候导致美国农作物保险中玉米损失概率翻倍:时空预测与可能的对策
arXiv - QuantFin - Risk Management Pub Date : 2024-08-05 DOI: arxiv-2408.02217
A Samuel Pottinger, Lawson Connor, Brookie Guzder-Williams, Maya Weltman-Fahs, Timothy Bowles
{"title":"Climate-Driven Doubling of Maize Loss Probability in U.S. Crop Insurance: Spatiotemporal Prediction and Possible Policy Responses","authors":"A Samuel Pottinger, Lawson Connor, Brookie Guzder-Williams, Maya Weltman-Fahs, Timothy Bowles","doi":"arxiv-2408.02217","DOIUrl":"https://doi.org/arxiv-2408.02217","url":null,"abstract":"Climate change not only threatens agricultural producers but also strains\u0000financial institutions. These important food system actors include government\u0000entities tasked with both insuring grower livelihoods and supporting response\u0000to continued global warming. We use an artificial neural network to predict\u0000future maize yields in the U.S. Corn Belt, finding alarming changes to\u0000institutional risk exposure within the Federal Crop Insurance Program.\u0000Specifically, our machine learning method anticipates more frequent and more\u0000severe yield losses that would result in the annual probability of Yield\u0000Protection (YP) claims to more than double at mid-century relative to\u0000simulations without continued climate change. Furthermore, our dual finding of\u0000relatively unchanged average yields paired with decreasing yield stability\u0000reveals targeted opportunities to adjust coverage formulas to include\u0000variability. This important structural shift may help regulators support grower\u0000adaptation to continued climate change by recognizing the value of\u0000risk-reducing strategies such as regenerative agriculture. Altogether, paired\u0000with open source interactive tools for deeper investigation, our risk profile\u0000simulations fill an actionable gap in current understanding, bridging granular\u0000historic yield estimation and climate-informed prediction of future\u0000insurer-relevant loss.","PeriodicalId":501128,"journal":{"name":"arXiv - QuantFin - Risk Management","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
How much should you pay for restaking security? 重塑安全系统需要支付多少费用?
arXiv - QuantFin - Risk Management Pub Date : 2024-08-01 DOI: arxiv-2408.00928
Tarun Chitra, Mallesh Pai
{"title":"How much should you pay for restaking security?","authors":"Tarun Chitra, Mallesh Pai","doi":"arxiv-2408.00928","DOIUrl":"https://doi.org/arxiv-2408.00928","url":null,"abstract":"Restaking protocols have aggregated billions of dollars of security by\u0000utilizing token incentives and payments. A natural question to ask is: How much\u0000security do restaked services emph{really} need to purchase? To answer this\u0000question, we expand a model of Durvasula and Roughgarden [DR24] that includes\u0000incentives and an expanded threat model consisting of strategic attackers and\u0000users. Our model shows that an adversary with a strictly submodular profit\u0000combined with strategic node operators who respond to incentives can avoid the\u0000large-scale cascading failures of~[DR24]. We utilize our model to construct an\u0000approximation algorithm for choosing token-based incentives that achieve a\u0000given security level against adversaries who are bounded in the number of\u0000services they can simultaneously attack. Our results suggest that incentivized\u0000restaking protocols can be secure with proper incentive management.","PeriodicalId":501128,"journal":{"name":"arXiv - QuantFin - Risk Management","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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