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Deep xVA Solver: A Neural Network–Based Counterparty Credit Risk Management Framework 深度xVA求解器:一个基于神经网络的交易对手信用风险管理框架
4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2023-03-30 DOI: 10.1137/21m1457606
Alessandro Gnoatto, Athena Picarelli, Christoph Reisinger
{"title":"Deep xVA Solver: A Neural Network–Based Counterparty Credit Risk Management Framework","authors":"Alessandro Gnoatto, Athena Picarelli, Christoph Reisinger","doi":"10.1137/21m1457606","DOIUrl":"https://doi.org/10.1137/21m1457606","url":null,"abstract":"In this paper, we present a novel computational framework for portfolio-wide risk management problems, where the presence of a potentially large number of risk factors makes traditional numerical techniques ineffective. The new method utilizes a coupled system of BSDEs for the valuation adjustments (xVA) and solves these by a recursive application of a neural network–based BSDE solver. This not only makes the computation of xVA for high-dimensional problems feasible, but also produces hedge ratios and dynamic risk measures for xVA, and allows simulations of the collateral account.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135950691","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: 9
Optimal Reinsurance to Minimize the Probability of Drawdown under the Mean-Variance Premium Principle: Asymptotic Analysis 均值-方差保费原则下最优赔付概率最小的再保险:渐近分析
4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2023-03-03 DOI: 10.1137/21m1461666
Pablo Azcue, Xiaoqing Liang, Nora Muler, Virginia R. Young
{"title":"Optimal Reinsurance to Minimize the Probability of Drawdown under the Mean-Variance Premium Principle: Asymptotic Analysis","authors":"Pablo Azcue, Xiaoqing Liang, Nora Muler, Virginia R. Young","doi":"10.1137/21m1461666","DOIUrl":"https://doi.org/10.1137/21m1461666","url":null,"abstract":"In this paper, we consider an optimal reinsurance problem to minimize the probability of drawdown for the scaled Cramér–Lundberg risk model when the reinsurance premium is computed according to the mean-variance premium principle. We extend the work of Liang, Liang, and Young [Insurance Math. Econom., 92 (2020), pp. 128–146] to the case of minimizing the probability of drawdown. By using the comparison method and the tool of adjustment coefficients, we show that the minimum probability of drawdown for the scaled classical risk model converges to the minimum probability for its diffusion approximation, and the rate of convergence is of order . We further show that using the optimal strategy from the diffusion approximation in the scaled classical risk model is -optimal.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134945916","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: 1
Bayesian Estimation and Optimization for Learning Sequential Regularized Portfolios 序列正则化组合学习的贝叶斯估计与优化
4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2023-01-27 DOI: 10.1137/21m1427176
Godeliva Petrina Marisu, Chi Seng Pun
{"title":"Bayesian Estimation and Optimization for Learning Sequential Regularized Portfolios","authors":"Godeliva Petrina Marisu, Chi Seng Pun","doi":"10.1137/21m1427176","DOIUrl":"https://doi.org/10.1137/21m1427176","url":null,"abstract":"This paper incorporates Bayesian estimation and optimization into a portfolio selection framework, particularly for high-dimensional portfolios in which the number of assets is larger than the number of observations. We leverage a constrained minimization approach, called the linear programming optimal (LPO) portfolio, to directly estimate effective parameters appearing in the optimal portfolio. We propose two refinements for the LPO strategy. First, we explore improved Bayesian estimates, instead of sample estimates, of the covariance matrix of asset returns. Second, we introduce Bayesian optimization (BO) to replace traditional grid-search cross-validation (CV) in tuning hyperparameters of the LPO strategy. We further propose modifications in the BO algorithm by (1) taking into account the time-dependent nature of financial problems and (2) extending the commonly used expected improvement acquisition function to include a tunable trade-off with the improvement’s variance. Allowing a general case of noisy observations, we theoretically derive the sublinear convergence rate of BO under the newly proposed EIVar and thus our algorithm has no regret. Our empirical studies confirm that the adjusted BO results in portfolios with higher out-of-sample Sharpe ratio, certainty equivalent, and lower turnover compared to those tuned with CV. This superior performance is achieved with a significant reduction in time elapsed, thus also addressing time-consuming issues of CV. Furthermore, LPO with Bayesian estimates outperforms the original proposal of LPO, as well as the benchmark equally weighted and plugin strategies.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135744712","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: 1
Competition in Fund Management and Forward Relative Performance Criteria 基金管理的竞争及远期相对业绩准则
IF 1 4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2022-10-04 DOI: 10.1137/20m1376169
Michail Anthropelos, Tianran Geng, Thaleia Zariphopoulou
{"title":"Competition in Fund Management and Forward Relative Performance Criteria","authors":"Michail Anthropelos, Tianran Geng, Thaleia Zariphopoulou","doi":"10.1137/20m1376169","DOIUrl":"https://doi.org/10.1137/20m1376169","url":null,"abstract":"SIAM Journal on Financial Mathematics, Volume 13, Issue 4, Page 1271-1301, December 2022. <br/> In an Itô-diffusion market, two fund managers trade under relative performance concerns. For both the asset specialization and diversification settings, we analyze the passive and competitive cases. We measure the performance of the managers' strategies via forward relative performance criteria, leading to the respective notions of forward best-response criterion and forward Nash equilibrium. The motivation to develop such criteria comes from the need to relax various crucial, but quite stringent for this problem, existing assumptions, such as the a priori choices of both the market model and the investment horizon, the commonality of the latter for both managers, as well as the full a priori knowledge of the competitor's policies for the best-response case. We focus on locally riskless criteria and deduce the random forward equations. We solve the CRRA cases and thus also extend the related results in the classical setting. An important by-product of the work herein is the development of forward performance criteria for investment problems in Itô-diffusion markets under the presence of correlated random endowment process for both the perfectly and incomplete market cases.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"22 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138520247","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
Escrow and Clawback 托管和收回
IF 1 4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2022-09-15 DOI: 10.1137/21m1455619
Steven Shreve, Jing Wang
{"title":"Escrow and Clawback","authors":"Steven Shreve, Jing Wang","doi":"10.1137/21m1455619","DOIUrl":"https://doi.org/10.1137/21m1455619","url":null,"abstract":"SIAM Journal on Financial Mathematics, Volume 13, Issue 3, Page 1191-1229, September 2022. <br/> Since the financial crisis of 2008, clawback provisions have been implemented by several high-profile banks and are also required by regulators in order to mitigate the cost of financial failures and to deter excessive risk taking. We construct a model to investigate the long-term effect on the bank's revenue of deferring (escrowing) a trader's bonuses to facilitate clawback. We formulate the question by setting up an infinite-horizon dynamic programming model. Within this model, the trader's optimal investment and consumption strategy, with and without bonus escrow, can be expressed by explicit analytic formulas. These formulas enable calculation and comparison of the bank's total expected revenue under the two bonus payout schemes. The results of the comparison depend on the parameters describing the trader's risk appetite, the discount factor, and the bank's level of patience, in addition to the market parameters. In particular, when the bank's total expected discounted revenue is finite under both types of bonus payment schemes and the bank is sufficiently patient, the bank benefits by escrowing the trader's bonus, although not escrowing the trader's bonus brings better short-term revenue.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"26 10","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138520277","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
Portfolio Management 项目组合管理
IF 1 4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2021-07-08 DOI: 10.1201/9780429503665-3
G. Campolieti, R. Makarov
{"title":"Portfolio Management","authors":"G. Campolieti, R. Makarov","doi":"10.1201/9780429503665-3","DOIUrl":"https://doi.org/10.1201/9780429503665-3","url":null,"abstract":"","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"64 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79732134","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
Single-Period Arrow–Debreu Models 单周期箭头-德布鲁模型
IF 1 4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2021-07-08 DOI: 10.1201/9780429503665-5
G. Campolieti, R. Makarov
{"title":"Single-Period Arrow–Debreu Models","authors":"G. Campolieti, R. Makarov","doi":"10.1201/9780429503665-5","DOIUrl":"https://doi.org/10.1201/9780429503665-5","url":null,"abstract":"","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"94 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80034286","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
Pricing high-dimensional Bermudan options with hierarchical tensor formats 用分层张量格式对高维百慕大期权进行定价
IF 1 4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2021-03-02 DOI: 10.1137/21m1402170
Christian Bayer, M. Eigel, Leon Sallandt, Philipp Trunschke
{"title":"Pricing high-dimensional Bermudan options with hierarchical tensor formats","authors":"Christian Bayer, M. Eigel, Leon Sallandt, Philipp Trunschke","doi":"10.1137/21m1402170","DOIUrl":"https://doi.org/10.1137/21m1402170","url":null,"abstract":"An efficient compression technique based on hierarchical tensors for popular option pricing methods is presented. It is shown that the\"curse of dimensionality\"can be alleviated for the computation of Bermudan option prices with the Monte Carlo least-squares approach as well as the dual martingale method, both using high-dimensional tensorized polynomial expansions. This discretization allows for a simple and computationally cheap evaluation of conditional expectations. Complexity estimates are provided as well as a description of the optimization procedures in the tensor train format. Numerical experiments illustrate the favourable accuracy of the proposed methods. The dynamical programming method yields results comparable to recent Neural Network based methods.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"abs/2103.01934 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2021-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64314418","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: 10
Credit Risk Propagation in Structural-Form Models 结构-形式模型中的信用风险传播
IF 1 4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2021-01-01 DOI: 10.1137/20m135340x
C. Fuh, C. Kao
{"title":"Credit Risk Propagation in Structural-Form Models","authors":"C. Fuh, C. Kao","doi":"10.1137/20m135340x","DOIUrl":"https://doi.org/10.1137/20m135340x","url":null,"abstract":"Existing empirical studies on correlated defaults have shown that the default of a firm impacts other firms; however, this impact has yet to be theoretically validated and quantified, especially un...","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"550 1","pages":"1340-1373"},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64311738","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: 1
Conditional Systemic Risk Measures 有条件系统性风险措施
IF 1 4区 经济学
SIAM Journal on Financial Mathematics Pub Date : 2020-10-22 DOI: 10.1137/20m1370616
A. Doldi, M. Frittelli
{"title":"Conditional Systemic Risk Measures","authors":"A. Doldi, M. Frittelli","doi":"10.1137/20m1370616","DOIUrl":"https://doi.org/10.1137/20m1370616","url":null,"abstract":"We investigate to which extent the relevant features of (static) systemic risk measures can be extended to a conditional setting. After providing a general dual representation result, we analyze in greater detail Conditional Shortfall Systemic Risk Measures. In the particular case of exponential preferences, we provide explicit formulas that also allow us to show a time consistency property. Finally, we provide an interpretation of the allocations associated to Conditional Shortfall Systemic Risk Measures as suitably defined equilibria. Conceptually, the generalization from static to conditional systemic risk measures can be achieved in a natural way, even though the proofs become more technical than in the unconditional framework.","PeriodicalId":48880,"journal":{"name":"SIAM Journal on Financial Mathematics","volume":"12 1","pages":"1459-1507"},"PeriodicalIF":1.0,"publicationDate":"2020-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64312557","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: 11
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