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On Robust Fundamental Theorems of Asset Pricing in Discrete Time 论离散时间资产定价的稳健基本定理
IF 1 4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2024-07-04 DOI: 10.1137/23m156032x
Huy N. Chau
{"title":"On Robust Fundamental Theorems of Asset Pricing in Discrete Time","authors":"Huy N. Chau","doi":"10.1137/23m156032x","DOIUrl":"https://doi.org/10.1137/23m156032x","url":null,"abstract":"SIAM Journal on Financial Mathematics, Volume 15, Issue 3, Page 571-600, September 2024. <br/> Abstract.This paper is devoted to a study of robust fundamental theorems of asset pricing in discrete time and finite horizon settings. Uncertainty is modeled by a (possibly uncountable) family of price processes on the same probability space. Our technical assumption is the continuity of the price processes with respect to uncertain parameters. In this setting, we introduce a new topological framework which allows us to use the classical arguments in arbitrage pricing theory involving Lp spaces, the Hahn–Banach separation theorem, and other tools from functional analysis. The first result is the equivalence of a “no robust arbitrage” condition and the existence of a new “robust pricing system.” The second result shows superhedging dualities and the existence of superhedging strategies without restrictive conditions on payoff functions, in contrast to other related studies. The third result discusses completeness in the present robust setting. When other options are available for static trading, we could reduce the set of robust pricing systems and hence the superhedging prices.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"46 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nonasymptotic Estimation of Risk Measures Using Stochastic Gradient Langevin Dynamics 利用随机梯度朗文动力学对风险度量进行非渐近估计
IF 1 4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2024-06-07 DOI: 10.1137/23m1552747
Jiarui Chu, Ludovic Tangpi
{"title":"Nonasymptotic Estimation of Risk Measures Using Stochastic Gradient Langevin Dynamics","authors":"Jiarui Chu, Ludovic Tangpi","doi":"10.1137/23m1552747","DOIUrl":"https://doi.org/10.1137/23m1552747","url":null,"abstract":"SIAM Journal on Financial Mathematics, Volume 15, Issue 2, Page 503-536, June 2024. <br/> Abstract.In this paper we will study the approximation of some law-invariant risk measures. As a starting point, we approximate the average value at risk using stochastic gradient Langevin dynamics, which can be seen as a variant of the stochastic gradient descent algorithm. Further, the Kusuoka spectral representation allows us to bootstrap the estimation of the average value at risk to extend the algorithm to general law-invariant risk measures. We will present both theoretical, nonasymptotic convergence rates of the approximation algorithm and numerical simulations.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"24 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Risk Measures beyond Frictionless Markets 无摩擦市场之外的风险措施
IF 1 4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2024-06-07 DOI: 10.1137/22m1540090
Maria Arduca, Cosimo Munari
{"title":"Risk Measures beyond Frictionless Markets","authors":"Maria Arduca, Cosimo Munari","doi":"10.1137/22m1540090","DOIUrl":"https://doi.org/10.1137/22m1540090","url":null,"abstract":"SIAM Journal on Financial Mathematics, Volume 15, Issue 2, Page 537-570, June 2024. <br/> Abstract.We develop a general theory of risk measures to determine the optimal amount of capital to raise and invest in a portfolio of reference traded securities in order to meet a prespecified regulatory requirement. The distinguishing feature of our approach is that we embed portfolio constraints and transaction costs into the securities market. As a consequence, the property of translation invariance, which plays a key role in the classical theory, ceases to hold. We provide a comprehensive analysis of relevant properties, such as star shapedness, positive homogeneity, convexity, quasiconvexity, subadditivity, and lower semicontinuity. In addition, we establish dual representations for convex and quasiconvex risk measures. In the convex case, the absence of a special kind of arbitrage opportunity allows one to obtain dual representations in terms of pricing rules that respect market bid-ask spreads and assign a strictly positive price to each nonzero position in the regulator’s acceptance set.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"17 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141506706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Short Communication: Monte Carlo Expected Wealth and Risk Measure Trade-Off Portfolio Optimization 简短交流：蒙特卡洛预期财富与风险度量权衡组合优化
IF 1 4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2024-06-03 DOI: 10.1137/23m1624439
Raino A. E. Mäkinen, Jari Toivanen
{"title":"Short Communication: Monte Carlo Expected Wealth and Risk Measure Trade-Off Portfolio Optimization","authors":"Raino A. E. Mäkinen, Jari Toivanen","doi":"10.1137/23m1624439","DOIUrl":"https://doi.org/10.1137/23m1624439","url":null,"abstract":"SIAM Journal on Financial Mathematics, Volume 15, Issue 2, Page SC41-SC53, June 2024. <br/> Abstract.A multiperiod portfolio optimization is described with Monte Carlo sampled risky asset paths under realistic constraints on the investment policies. The proposed approach can be used with various asset and risk models. It is flexible as it does not require dynamic programming or any transformations. As examples, the variance and semivariance risks are considered leading to mean-variance and mean-semivariance formulations, respectively. A quasi-Newton method with an adjoint gradient computation can solve the resulting optimization problems efficiently. Numerical examples show efficient frontiers together with optimal asset allocations computed for mean-variance and mean-semivariance portfolios with two and five assets.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"37 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141257589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal Clearing Payments in a Financial Contagion Model 金融疫情模型中的最优清算支付
IF 1 4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2024-06-03 DOI: 10.1137/22m150294x
Giuseppe C. Calafiore, Giulia Fracastoro, Anton V. Proskurnikov
{"title":"Optimal Clearing Payments in a Financial Contagion Model","authors":"Giuseppe C. Calafiore, Giulia Fracastoro, Anton V. Proskurnikov","doi":"10.1137/22m150294x","DOIUrl":"https://doi.org/10.1137/22m150294x","url":null,"abstract":"SIAM Journal on Financial Mathematics, Volume 15, Issue 2, Page 473-502, June 2024. <br/> Abstract.Financial networks are characterized by complex structures of mutual obligations. These obligations are fulfilled entirely or in part (when defaults occur) via a mechanism called clearing, which determines a set of payments that settle the claims by respecting rules such as limited liability, absolute priority, and proportionality (pro-rated payments). In the presence of shocks on the financial system, however, the clearing mechanism may lead to cascaded defaults and eventually to financial disaster. In this paper, we first study the clearing model under pro-rated payments of Eisenberg and Noe, and we derive novel necessary and sufficient conditions for the uniqueness of the clearing payments, valid for an arbitrary topology of the financial network. Next, we observe that the proportionality rule is a factor that potentially concurs to the cascaded defaults effect, and that the aggregated systemic loss can be reduced if this rule is lifted. We thus shift the focus from the individual interest to the overall systemic interest to contain the adverse effects of cascaded failures, and we show that pro-rate-free clearing payments can be computed uniquely by solving suitable convex optimization problems.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"39 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Detecting Data-Driven Robust Statistical Arbitrage Strategies with Deep Neural Networks 利用深度神经网络检测数据驱动的稳健统计套利策略
IF 1 4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2024-05-30 DOI: 10.1137/22m1487928
Ariel Neufeld, Julian Sester, Daiying Yin
{"title":"Detecting Data-Driven Robust Statistical Arbitrage Strategies with Deep Neural Networks","authors":"Ariel Neufeld, Julian Sester, Daiying Yin","doi":"10.1137/22m1487928","DOIUrl":"https://doi.org/10.1137/22m1487928","url":null,"abstract":"SIAM Journal on Financial Mathematics, Volume 15, Issue 2, Page 436-472, June 2024. <br/> Abstract.We present an approach, based on deep neural networks, for identifying robust statistical arbitrage strategies in financial markets. Robust statistical arbitrage strategies refer to trading strategies that enable profitable trading under model ambiguity. The presented novel methodology allows one to consider a large amount of underlying securities simultaneously and does not depend on the identification of cointegrated pairs of assets; hence it is applicable on high-dimensional financial markets or in markets where classical pairs trading approaches fail. Moreover, we provide a method to build an ambiguity set of admissible probability measures that can be derived from observed market data. Thus, the approach can be considered as being model free and entirely data driven. We showcase the applicability of our method by providing empirical investigations with highly profitable trading performances even in 50 dimensions, during financial crises, and when the cointegration relationship between asset pairs stops to persist.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"25 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141165744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fully Dynamic Risk Measures: Horizon Risk, Time-Consistency, and Relations with BSDEs and BSVIEs 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区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2024-05-21 DOI: 10.1137/23m1546804
Giulia Di Nunno, Emanuela Rosazza Gianin
{"title":"Fully Dynamic Risk Measures: Horizon Risk, Time-Consistency, and Relations with BSDEs and BSVIEs","authors":"Giulia Di Nunno, Emanuela Rosazza Gianin","doi":"10.1137/23m1546804","DOIUrl":"https://doi.org/10.1137/23m1546804","url":null,"abstract":"SIAM Journal on Financial Mathematics, Volume 15, Issue 2, Page 399-435, June 2024. <br/> 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.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141150047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Short Communication: Utility-Based Acceptability Indices 简短交流：基于效用的可接受性指数
IF 1 4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2024-05-14 DOI: 10.1137/24m1632486
Marcin Pitera, Miklós Rásonyi
{"title":"Short Communication: Utility-Based Acceptability Indices","authors":"Marcin Pitera, Miklós Rásonyi","doi":"10.1137/24m1632486","DOIUrl":"https://doi.org/10.1137/24m1632486","url":null,"abstract":"SIAM Journal on Financial Mathematics, Volume 15, Issue 2, Page SC28-SC40, June 2024. <br/> Abstract.This paper presents a novel class of performance measures that is constituted by certainty equivalents derived from scaled utility functions. We examine the characteristics of these measures and demonstrate that while most normative properties from the coherent acceptability framework are preserved, scale invariance is replaced by inverse positive homogeneity; this property is a specific type of subscale invariance. Additionally, we show that the introduced framework is suited for log-return portfolio optimization, as the corresponding problem admits a solution under generic conditions.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"19 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Relative Wealth Concerns with Partial Information and Heterogeneous Priors 部分信息和异质先验的相对财富考量
IF 1 4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2024-04-29 DOI: 10.1137/22m1508625
Chao Deng, Xizhi Su, Chao Zhou
{"title":"Relative Wealth Concerns with Partial Information and Heterogeneous Priors","authors":"Chao Deng, Xizhi Su, Chao Zhou","doi":"10.1137/22m1508625","DOIUrl":"https://doi.org/10.1137/22m1508625","url":null,"abstract":"SIAM Journal on Financial Mathematics, Volume 15, Issue 2, Page 360-398, June 2024. <br/>Abstract.We establish a Nash equilibrium for [math] agents with the relative wealth performance criteria when the market return is unobservable. We show that the optimal investment strategy under a stochastic return rate model can be characterized by a fully coupled forward-backward stochastic differential equation (FBSDE). We establish the existence and uniqueness results for the class of FBSDEs with stochastic coefficients and solve the utility game under partial information by using deep neural networks. We demonstrate the efficiency and accuracy by a base-case comparison with the semianalytical solution in the linear case. We examined the Sharpe ratios and the variance risk ratios by numerical simulation. We observe that the agent with the most accurate prior estimate is likely to lead the herd. Moreover, the effect of competition on heterogeneous agents varies more with market characteristics compared to that of the homogeneous case.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"65 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140809547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mortgage Contracts and Underwater Default 抵押合同和水下违约
IF 1 4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2024-04-11 DOI: 10.1137/22m1498590
Yerkin Kitapbayev, Scott Robertson
{"title":"Mortgage Contracts and Underwater Default","authors":"Yerkin Kitapbayev, Scott Robertson","doi":"10.1137/22m1498590","DOIUrl":"https://doi.org/10.1137/22m1498590","url":null,"abstract":"SIAM Journal on Financial Mathematics, Volume 15, Issue 2, Page 315-359, June 2024. <br/>Abstract.We analyze recently proposed mortgage contracts that aim to eliminate selective borrower default when the loan balance exceeds the house price (the “underwater” effect). We show contracts that automatically reduce the outstanding balance in the event of house price decline do eliminate selective default, but they may induce prepayment in low price states. However, low state prepayments vanish if the benefit from home ownership is sufficiently high. We also show that capital gain sharing features, such as prepayment penalties in high house price states, are ineffective as they virtually eliminate prepayment. For observed foreclosure costs, we find that contracts with automatic balance adjustments become preferable to the traditional fixed-rate contracts at mortgage rate spreads between 20–50 basis points. We obtain these results for perpetual versions of the contracts using an American options pricing methodology, in a continuous-time model with diffusive home prices. The contracts’ values and decision rules are associated with free boundary problems, which admit semiexplicit solutions.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"77 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140600530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","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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