arXiv - QuantFin - Mathematical Finance最新文献_第2页

A robust stochastic control problem with applications to monotone mean-variance problems 稳健随机控制问题与单调均值方差问题的应用

arXiv - QuantFin - Mathematical Finance Pub Date : 2024-08-16 DOI: arxiv-2408.08595

Yuyang Chen, Tianjiao Hua, Peng Luo

引用次数: 0

The mean-variance portfolio selection based on the average and current profitability of the risky asset 根据风险资产的平均收益率和当前收益率选择均值-方差投资组合

arXiv - QuantFin - Mathematical Finance Pub Date : 2024-08-15 DOI: arxiv-2408.07969

Yu Li, Yuhan Wu, Shuhua Zhang

引用次数: 0

Endogenous Crashes as Phase Transitions 作为阶段转换的内生性崩溃

arXiv - QuantFin - Mathematical Finance Pub Date : 2024-08-12 DOI: arxiv-2408.06433

Revant Nayar, Minhajul Islam

{"title":"Endogenous Crashes as Phase Transitions","authors":"Revant Nayar, Minhajul Islam","doi":"arxiv-2408.06433","DOIUrl":"https://doi.org/arxiv-2408.06433","url":null,"abstract":"This paper explores the mechanisms behind extreme financial events,\u0000specifically market crashes, by employing the theoretical framework of phase\u0000transitions. We focus on endogenous crashes, driven by internal market\u0000dynamics, and model these events as first-order phase transitions critical,\u0000stochastic, and dynamic. Through a comparative analysis of early warning\u0000signals associated with each type of transition, we demonstrate that dynamic\u0000phase transitions (DPT) offer a more accurate representation of market crashes\u0000than critical (CPT) or stochastic phase transitions (SPT). Unlike existing\u0000models, such as the Log-Periodic Power Law (LPPL) model, which often suffers\u0000from overfitting and false positives, our approach grounded in DPT provides a\u0000more robust prediction framework. Empirical findings, based on an analysis of\u0000S&P 500 stocks from 2019 to 2024, reveal significant trends in volatility and\u0000anomalous dimensions before crashes, supporting the superiority of the DPT\u0000model. This work contributes to a deeper understanding of the predictive\u0000signals preceding market crashes and offers a novel perspective on their\u0000underlying dynamics.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142216347","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

Linear reflected backward stochastic differential equations arising from vulnerable claims in markets with random horizon 具有随机地平线的市场中脆弱索赔所产生的线性反射后向随机微分方程

arXiv - QuantFin - Mathematical Finance Pub Date : 2024-08-08 DOI: arxiv-2408.04758

T. Choulli, S. Alsheyab

{"title":"Linear reflected backward stochastic differential equations arising from vulnerable claims in markets with random horizon","authors":"T. Choulli, S. Alsheyab","doi":"arxiv-2408.04758","DOIUrl":"https://doi.org/arxiv-2408.04758","url":null,"abstract":"This paper considers the setting governed by $(mathbb{F},tau)$, where\u0000$mathbb{F}$ is the \"public\" flow of information, and $tau$ is a random time\u0000which might not be $mathbb{F}$-observable. This framework covers credit risk\u0000theory and life insurance. In this setting, we assume $mathbb{F}$ being\u0000generated by a Brownian motion $W$ and consider a vulnerable claim $xi$, whose\u0000payment's policy depends {it{essentially}} on the occurrence of $tau$. The\u0000hedging problems, in many directions, for this claim led to the question of\u0000studying the linear reflected-backward-stochastic differential equations (RBSDE\u0000hereafter), begin{equation*} begin{split}\u0000&dY_t=f(t)d(twedgetau)+Z_tdW_{twedge{tau}}+dM_t-dK_t,quad Y_{tau}=xi,\u0000& Ygeq Squadmbox{on}quad Lbrack0,tauLbrack,quad\u0000displaystyleint_0^{tau}(Y_{s-}-S_{s-})dK_s=0quad Pmbox{-a.s.}.end{split}\u0000end{equation*} This is the objective of this paper. For this RBSDE and without\u0000any further assumption on $tau$ that might neglect any risk intrinsic to its\u0000stochasticity, we answer the following: a) What are the sufficient minimal\u0000conditions on the data $(f, xi, S, tau)$ that guarantee the existence of the\u0000solution to this RBSDE? b) How can we estimate the solution in norm using $(f,\u0000xi, S)$? c) Is there an $mathbb F$-RBSDE that is intimately related to the\u0000current one and how their solutions are related to each other? This latter\u0000question has practical and theoretical leitmotivs.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"65 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947294","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

Efficient simulation of the SABR model 高效模拟 SABR 模型

arXiv - QuantFin - Mathematical Finance Pub Date : 2024-08-04 DOI: arxiv-2408.01898

Jaehyuk Choi, Lilian Hu, Yue Kuen Kwok

{"title":"Efficient simulation of the SABR model","authors":"Jaehyuk Choi, Lilian Hu, Yue Kuen Kwok","doi":"arxiv-2408.01898","DOIUrl":"https://doi.org/arxiv-2408.01898","url":null,"abstract":"We propose an efficient and reliable simulation scheme for the\u0000stochastic-alpha-beta-rho (SABR) model. The two challenges of the SABR\u0000simulation lie in sampling (i) the integrated variance conditional on terminal\u0000volatility and (ii) the terminal price conditional on terminal volatility and\u0000integrated variance. For the first sampling procedure, we analytically derive\u0000the first four moments of the conditional average variance, and sample it from\u0000the moment-matched shifted lognormal approximation. For the second sampling\u0000procedure, we approximate the conditional terminal price as a\u0000constant-elasticity-of-variance (CEV) distribution. Our CEV approximation\u0000preserves the martingale condition and precludes arbitrage, which is a key\u0000advantage over Islah's approximation used in most SABR simulation schemes in\u0000the literature. Then, we adopt the exact sampling method of the CEV\u0000distribution based on the shifted-Poisson-mixture Gamma random variable. Our\u0000enhanced procedures avoid the tedious Laplace inversion algorithm for sampling\u0000integrated variance and non-efficient inverse transform sampling of the forward\u0000price in some of the earlier simulation schemes. Numerical results demonstrate\u0000our simulation scheme to be highly efficient, accurate, and reliable.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947296","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

A Path Integral Approach for Time-Dependent Hamiltonians with Applications to Derivatives Pricing 与时间相关的哈密顿模型的路径积分法及其在衍生品定价中的应用

arXiv - QuantFin - Mathematical Finance Pub Date : 2024-08-04 DOI: arxiv-2408.02064

Mark Stedman, Luca Capriotti

引用次数: 0

The indifference value of the weak information 弱信息的冷漠值

arXiv - QuantFin - Mathematical Finance Pub Date : 2024-08-04 DOI: arxiv-2408.02137

Fabrice Baudoin, Oleksii Mostovyi

引用次数: 0

Generative model for financial time series trained with MMD using a signature kernel 使用特征核的 MMD 训练金融时间序列生成模型

arXiv - QuantFin - Mathematical Finance Pub Date : 2024-07-29 DOI: arxiv-2407.19848

Lu Chung I, Julian Sester

{"title":"Generative model for financial time series trained with MMD using a signature kernel","authors":"Lu Chung I, Julian Sester","doi":"arxiv-2407.19848","DOIUrl":"https://doi.org/arxiv-2407.19848","url":null,"abstract":"Generating synthetic financial time series data that accurately reflects\u0000real-world market dynamics holds tremendous potential for various applications,\u0000including portfolio optimization, risk management, and large scale machine\u0000learning. We present an approach for training generative models for financial\u0000time series using the maximum mean discrepancy (MMD) with a signature kernel.\u0000Our method leverages the expressive power of the signature transform to capture\u0000the complex dependencies and temporal structures inherent in financial data. We\u0000employ a moving average model to model the variance of the noise input,\u0000enhancing the model's ability to reproduce stylized facts such as volatility\u0000clustering. Through empirical experiments on S&P 500 index data, we demonstrate\u0000that our model effectively captures key characteristics of financial time\u0000series and outperforms a comparable GAN-based approach. In addition, we explore\u0000the application of the synthetic data generated to train a reinforcement\u0000learning agent for portfolio management, achieving promising results. Finally,\u0000we propose a method to add robustness to the generative model by tweaking the\u0000noise input so that the generated sequences can be adjusted to different market\u0000environments with minimal data.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141863627","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

Consumption-investment optimization with Epstein-Zin utility in unbounded non-Markovian markets 无约束非马尔可夫市场中具有爱泼斯坦-津效用的消费-投资优化

arXiv - QuantFin - Mathematical Finance Pub Date : 2024-07-29 DOI: arxiv-2407.19995

Zixin Feng, Dejian Tian, Harry Zheng

引用次数: 0

The Gradient Flow of the Bass Functional in Martingale Optimal Transport 马丁格尔最优传输中巴斯函数的梯度流

arXiv - QuantFin - Mathematical Finance Pub Date : 2024-07-26 DOI: arxiv-2407.18781

Julio Backhoff-Veraguas, Gudmund Pammer, Walter Schachermayer

引用次数: 0