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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 Q3 BUSINESS, FINANCE Pub Date : 2023-03-30 DOI: 10.1137/21m1457606
Alessandro Gnoatto, Athena Picarelli, Christoph Reisinger
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.
在本文中,我们提出了一个新的计算框架,用于投资组合范围的风险管理问题,其中潜在的大量风险因素的存在使得传统的数值技术无效。该方法利用BSDE的耦合系统进行估值调整(xVA),并通过基于神经网络的BSDE求解器的递归应用来解决这些问题。这不仅使计算高维问题的xVA变得可行,而且还产生了xVA的对冲比率和动态风险度量,并允许模拟抵押品账户。
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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 Q3 BUSINESS, FINANCE Pub Date : 2023-03-03 DOI: 10.1137/21m1461666
Pablo Azcue, Xiaoqing Liang, Nora Muler, Virginia R. Young
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.
在本文中,我们考虑了一个最优再保险问题,当按均值-方差保费原则计算再保险保费时,缩放的cram r - lundberg风险模型的最优再保险问题是使赔付概率最小化。我们扩展了Liang, Liang, and Young [Insurance Math]的工作。的经济。, 92 (2020), pp. 128-146]最小化缩编概率的情况。通过比较方法和调整系数的工具,证明了经典风险模型的最小下降概率收敛于其扩散近似的最小概率,并且收敛速度是有阶的。进一步证明了在经典风险模型中使用扩散近似的最优策略是-最优的。
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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 Q3 BUSINESS, FINANCE Pub Date : 2023-01-27 DOI: 10.1137/21m1427176
Godeliva Petrina Marisu, Chi Seng Pun
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.
本文将贝叶斯估计和优化纳入到一个投资组合选择框架中,特别是对于资产数量大于观测数量的高维投资组合。我们利用一种称为线性规划最优(LPO)投资组合的约束最小化方法来直接估计最优投资组合中出现的有效参数。我们对LPO策略提出了两个改进方案。首先,我们探讨了资产收益协方差矩阵的改进贝叶斯估计,而不是样本估计。其次,我们引入贝叶斯优化(BO)来取代传统的网格搜索交叉验证(CV)来调整LPO策略的超参数。我们进一步提出对BO算法的修改:(1)考虑到财务问题的时间依赖性;(2)扩展常用的期望改进获取函数,以包括与改进方差的可调权衡。在考虑噪声观测的一般情况下,我们从理论上推导出了新提出的EIVar下BO的次线性收敛速率,从而使我们的算法没有遗憾。我们的实证研究证实,与使用CV调整的投资组合相比,调整后的BO导致投资组合具有更高的样本外夏普比率、确定性当量和更低的周转率。这种优越的性能是通过显著减少时间流逝来实现的,因此也解决了CV的耗时问题。此外,具有贝叶斯估计的LPO优于原始的LPO,以及基准等加权和插件策略。
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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 Q3 BUSINESS, FINANCE Pub Date : 2022-10-04 DOI: 10.1137/20m1376169
Michail Anthropelos, Tianran Geng, Thaleia Zariphopoulou
SIAM Journal on Financial Mathematics, Volume 13, Issue 4, Page 1271-1301, December 2022.
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.
《金融数学学报》,第13卷,第4期,1271-1301页,2022年12月。在Itô-diffusion市场中,两家基金管理公司在相对的业绩担忧下进行交易。在资产专业化和多元化两种情况下,我们分别分析了被动和竞争两种情况。我们通过前瞻性相对绩效标准来衡量管理者战略的绩效,从而得出各自的前瞻性最佳对策标准和前瞻性纳什均衡的概念。制定这种标准的动机来自于需要放松各种关键的,但对这个问题相当严格的现有假设,例如市场模型和投资范围的先验选择,后者对两位经理的共性,以及对最佳反应情况的竞争对手政策的全部先验知识。我们关注局部无风险准则,并推导出随机正演方程。我们解决了CRRA案例,从而扩展了经典环境下的相关结果。本文工作的一个重要副产品是在完全和不完全市场情况下,在相关随机禀赋过程存在的情况下,为Itô-diffusion市场的投资问题制定了前瞻性绩效标准。
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引用次数: 0
Escrow and Clawback 托管和收回
IF 1 4区 经济学 Q3 BUSINESS, FINANCE Pub Date : 2022-09-15 DOI: 10.1137/21m1455619
Steven Shreve, Jing Wang
SIAM Journal on Financial Mathematics, Volume 13, Issue 3, Page 1191-1229, September 2022.
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.
《金融数学学报》,第13卷,第3期,1191-1229页,2022年9月。自2008年金融危机以来,几家知名银行实施了追回条款,监管机构也要求这些条款,以减轻金融破产的成本,并阻止过度冒险。我们构建了一个模型来研究延迟(托管)交易员奖金以促进追回对银行收入的长期影响。我们通过建立一个无限视界动态规划模型来表达这个问题。在该模型中,交易者的最优投资和消费策略,在有和没有奖金托管的情况下,可以用显式的分析公式表示。这些公式可以计算和比较银行在两种奖金支付方案下的总预期收入。除了市场参数之外,比较的结果还取决于描述交易者风险偏好的参数、贴现因子和银行的耐心水平。特别是,当银行在两种奖金支付方案下的总预期贴现收益都是有限的,并且银行有足够的耐心时,银行通过托管交易员的奖金获利,尽管不托管交易员的奖金会带来更好的短期收益。
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引用次数: 0
Portfolio Management 项目组合管理
IF 1 4区 经济学 Q3 BUSINESS, FINANCE Pub Date : 2021-07-08 DOI: 10.1201/9780429503665-3
G. Campolieti, R. Makarov
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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 Q3 BUSINESS, FINANCE Pub Date : 2021-07-08 DOI: 10.1201/9780429503665-5
G. Campolieti, R. Makarov
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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 Q3 BUSINESS, FINANCE Pub Date : 2021-03-02 DOI: 10.1137/21m1402170
Christian Bayer, M. Eigel, Leon Sallandt, Philipp Trunschke
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.
针对目前流行的期权定价方法,提出了一种基于层次张量的有效压缩技术。研究表明,蒙特卡洛最小二乘法和对偶鞅方法均采用高维张紧多项式展开,可以缓解百慕大期权价格计算的“维数诅咒”。这种离散化允许对条件期望进行简单且计算成本低廉的评估。复杂性估计提供以及在张量列车格式的优化过程的描述。数值实验表明,所提方法具有良好的精度。动态规划方法的结果可与最近基于神经网络的方法相媲美。
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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 Q3 BUSINESS, FINANCE Pub Date : 2021-01-01 DOI: 10.1137/20m135340x
C. Fuh, C. Kao
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...
已有的相关违约实证研究表明,企业违约会对其他企业产生影响;然而,这种影响尚未在理论上得到验证和量化,特别是在…
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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 Q3 BUSINESS, FINANCE Pub Date : 2020-10-22 DOI: 10.1137/20m1370616
A. Doldi, M. Frittelli
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.
我们调查(静态)系统风险措施的相关特征在多大程度上可以扩展到条件设置。在提供一般的对偶表示结果之后,我们更详细地分析了条件短缺系统风险度量。在指数偏好的特殊情况下,我们提供了显式公式,也允许我们显示时间一致性。最后,我们提供了与条件短缺系统风险措施相关的分配作为适当定义的均衡的解释。从概念上讲,从静态到有条件的系统风险措施的概括可以以自然的方式实现,即使证明比无条件框架更具技术性。
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引用次数: 11
期刊
SIAM Journal on Financial Mathematics
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