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Optimal Trade Characterizations in Multi-Asset Crypto-Financial Markets 多资产加密金融市场中的最优交易特征描述
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-05-10 DOI: arxiv-2405.06854
C. Escudero, F. Lara, M. Sama
{"title":"Optimal Trade Characterizations in Multi-Asset Crypto-Financial Markets","authors":"C. Escudero, F. Lara, M. Sama","doi":"arxiv-2405.06854","DOIUrl":"https://doi.org/arxiv-2405.06854","url":null,"abstract":"This work focuses on the mathematical study of constant function market\u0000makers. We rigorously establish the conditions for optimal trading under the\u0000assumption of a quasilinear, but not necessarily convex (or concave), trade\u0000function. This generalizes previous results that used convexity, and also\u0000guarantees the robustness against arbitrage of so-designed automatic market\u0000makers. The theoretical results are illustrated by families of examples given\u0000by generalized means, and also by numerical simulations in certain concrete\u0000cases. These simulations along with the mathematical analysis suggest that the\u0000quasilinear-trade-function based automatic market makers might replicate the\u0000functioning of those based on convex functions, in particular regarding their\u0000resilience to arbitrage.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140939170","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 Two-layer Stochastic Game Approach to Reinsurance Contracting and Competition 再保险合同与竞争的双层随机博弈方法
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-05-10 DOI: arxiv-2405.06235
Zongxia Liang, Yi Xia, Bin Zou
{"title":"A Two-layer Stochastic Game Approach to Reinsurance Contracting and Competition","authors":"Zongxia Liang, Yi Xia, Bin Zou","doi":"arxiv-2405.06235","DOIUrl":"https://doi.org/arxiv-2405.06235","url":null,"abstract":"We introduce a two-layer stochastic game model to study reinsurance\u0000contracting and competition in a market with one insurer and two competing\u0000reinsurers. The insurer negotiates with both reinsurers simultaneously for proportional\u0000reinsurance contracts that are priced using the variance premium principle; the\u0000reinsurance contracting between the insurer and each reinsurer is modeled as a\u0000Stackelberg game. The two reinsurers compete for business from the insurer and optimize the\u0000so-called relative performance, instead of their own surplus; the competition\u0000game between the two reinsurers is settled by a non-cooperative Nash game. We\u0000obtain a sufficient and necessary condition, related to the competition degrees\u0000of the two reinsurers, for the existence of an equilibrium. We show that the\u0000equilibrium, if exists, is unique, and the equilibrium strategy of each player\u0000is constant, fully characterized in semi-closed form. Additionally, we obtain interesting sensitivity results for the equilibrium\u0000strategies through both an analytical and numerical study.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140939161","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
Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs with infinite activity 非线性抛物 PDE 和无限活动 PIDE 的随机深度分裂方法的全误差分析
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-05-08 DOI: arxiv-2405.05192
Ariel Neufeld, Philipp Schmocker, Sizhou Wu
{"title":"Full error analysis of the random deep splitting method for nonlinear parabolic PDEs and PIDEs with infinite activity","authors":"Ariel Neufeld, Philipp Schmocker, Sizhou Wu","doi":"arxiv-2405.05192","DOIUrl":"https://doi.org/arxiv-2405.05192","url":null,"abstract":"In this paper, we present a randomized extension of the deep splitting\u0000algorithm introduced in [Beck, Becker, Cheridito, Jentzen, and Neufeld (2021)]\u0000using random neural networks suitable to approximately solve both\u0000high-dimensional nonlinear parabolic PDEs and PIDEs with jumps having\u0000(possibly) infinite activity. We provide a full error analysis of our so-called\u0000random deep splitting method. In particular, we prove that our random deep\u0000splitting method converges to the (unique viscosity) solution of the nonlinear\u0000PDE or PIDE under consideration. Moreover, we empirically analyze our random\u0000deep splitting method by considering several numerical examples including both\u0000nonlinear PDEs and nonlinear PIDEs relevant in the context of pricing of\u0000financial derivatives under default risk. In particular, we empirically\u0000demonstrate in all examples that our random deep splitting method can\u0000approximately solve nonlinear PDEs and PIDEs in 10'000 dimensions within\u0000seconds.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140939543","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
Inflation Models with Correlation and Skew 具有相关性和偏斜性的通货膨胀模型
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-05-08 DOI: arxiv-2405.05101
Orcan Ogetbil, Bernhard Hientzsch
{"title":"Inflation Models with Correlation and Skew","authors":"Orcan Ogetbil, Bernhard Hientzsch","doi":"arxiv-2405.05101","DOIUrl":"https://doi.org/arxiv-2405.05101","url":null,"abstract":"We formulate a forward inflation index model with multi-factor volatility\u0000structure featuring a parametric form that allows calibration to correlations\u0000between indices of different tenors observed in the market. Assuming the\u0000nominal interest rate follows a single factor Gaussian short rate model, we\u0000present analytical prices for zero-coupon and year-on-year swaps, caps, and\u0000floors. The same method applies to any interest rate model for which one can\u0000compute the zero-coupon bond prices and measure shifts. We extend the\u0000multi-factor model with leverage functions to capture the entire market\u0000volatility skew with a single process. The time-consuming calibration step of\u0000this model can be avoided in the simplified model that we further propose. We\u0000demonstrate the leveraged and the simplified models with market data.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140939542","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
Despite Absolute Information Advantages, All Investors Incur Welfare Loss 尽管拥有绝对的信息优势，但所有投资者都会遭受福利损失
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-05-07 DOI: arxiv-2405.08822
Zongxia Liang, Qi Ye
{"title":"Despite Absolute Information Advantages, All Investors Incur Welfare Loss","authors":"Zongxia Liang, Qi Ye","doi":"arxiv-2405.08822","DOIUrl":"https://doi.org/arxiv-2405.08822","url":null,"abstract":"This paper delves into financial markets that incorporate a novel form of\u0000heterogeneity among investors, specifically in terms of their beliefs regarding\u0000the reliability of signals in the business cycle economy model, which may be\u0000biased. Unlike most papers in this field, we not only analyze the equilibrium\u0000but also examine welfare using objective measures while investors aim to\u0000maximize their utility based on subjective measures. Furthermore, we introduce\u0000passive investors and use their utility as a benchmark, thereby revealing the\u0000phenomenon of double loss sometimes. In the analysis, we examine two effects:\u0000the distortion effect on total welfare and the advantage effect of information\u0000and highlight their key factors of influence, with a particular emphasis on the\u0000proportion of investors. We also demonstrate that manipulating investors'\u0000estimation towards the economy can be a way to improve utility and identify an\u0000inner connection between welfare and survival.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"121 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060897","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
On variable annuities with surrender charges 关于有退保费用的变额年金
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-05-03 DOI: arxiv-2405.02115
Tiziano De Angelis, Alessandro Milazzo, Gabriele Stabile
{"title":"On variable annuities with surrender charges","authors":"Tiziano De Angelis, Alessandro Milazzo, Gabriele Stabile","doi":"arxiv-2405.02115","DOIUrl":"https://doi.org/arxiv-2405.02115","url":null,"abstract":"In this paper we provide a theoretical analysis of Variable Annuities with a\u0000focus on the holder's right to an early termination of the contract. We obtain\u0000a rigorous pricing formula and the optimal exercise boundary for the surrender\u0000option. We also illustrate our theoretical results with extensive numerical\u0000experiments. The pricing problem is formulated as an optimal stopping problem\u0000with a time-dependent payoff which is discontinuous at the maturity of the\u0000contract and non-smooth. This structure leads to non-monotonic optimal stopping\u0000boundaries which we prove nevertheless to be continuous and regular in the\u0000sense of diffusions for the stopping set. The lack of monotonicity of the\u0000boundary makes it impossible to use classical methods from optimal stopping.\u0000Also more recent results about Lipschitz continuous boundaries are not\u0000applicable in our setup. Thus, we contribute a new methodology for non-monotone\u0000stopping boundaries.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"139 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140939171","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
Mathematics of Differential Machine Learning in Derivative Pricing and Hedging 衍生品定价和对冲中的差分机器学习数学
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-05-02 DOI: arxiv-2405.01233
Pedro Duarte Gomes
{"title":"Mathematics of Differential Machine Learning in Derivative Pricing and Hedging","authors":"Pedro Duarte Gomes","doi":"arxiv-2405.01233","DOIUrl":"https://doi.org/arxiv-2405.01233","url":null,"abstract":"This article introduces the groundbreaking concept of the financial\u0000differential machine learning algorithm through a rigorous mathematical\u0000framework. Diverging from existing literature on financial machine learning,\u0000the work highlights the profound implications of theoretical assumptions within\u0000financial models on the construction of machine learning algorithms. This endeavour is particularly timely as the finance landscape witnesses a\u0000surge in interest towards data-driven models for the valuation and hedging of\u0000derivative products. Notably, the predictive capabilities of neural networks\u0000have garnered substantial attention in both academic research and practical\u0000financial applications. The approach offers a unified theoretical foundation that facilitates\u0000comprehensive comparisons, both at a theoretical level and in experimental\u0000outcomes. Importantly, this theoretical grounding lends substantial weight to\u0000the experimental results, affirming the differential machine learning method's\u0000optimality within the prevailing context. By anchoring the insights in rigorous mathematics, the article bridges the\u0000gap between abstract financial concepts and practical algorithmic\u0000implementations.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140828404","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
DeFi's Concentrated Liquidity From Scratch DeFi 从无到有的集中流动性
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-04-30 DOI: arxiv-2407.02496
Mark B. Richardson, Stefan Loesch
{"title":"DeFi's Concentrated Liquidity From Scratch","authors":"Mark B. Richardson, Stefan Loesch","doi":"arxiv-2407.02496","DOIUrl":"https://doi.org/arxiv-2407.02496","url":null,"abstract":"The scope of this article includes the three preeminent descriptions of\u0000concentrated liquidity from Bancor (2020 and 2022), and Uniswap (2021), as well\u0000as three additional descriptions informed by trigonometric analysis of the\u0000same. The purpose of this contribution is to organize the seminal and\u0000derivative forms of this cornerstone DeFi technology, and algebraically and\u0000geometrically elaborate these descriptions to achieve an authoritative and\u0000near-exhaustive overview of the underlying theory powering the current\u0000state-of-the-art in decentralized exchange infrastructure. This material was created for the Token Engineering Academy Study Season\u00002024, a cohort-based online program scheduled for April-July 2024. The Study\u0000Season offers access to a bachelor-level online learning program, and\u0000complementary live tracks with the most influential practitioners and\u0000researchers in the sector - all provided as free, public goods.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548013","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 pure dual approach for hedging Bermudan options 百慕大期权对冲的纯粹二元方法
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-04-29 DOI: arxiv-2404.18761
Aurélien Alfonsi, Ahmed Kebaier, Jérôme Lelong
{"title":"A pure dual approach for hedging Bermudan options","authors":"Aurélien Alfonsi, Ahmed Kebaier, Jérôme Lelong","doi":"arxiv-2404.18761","DOIUrl":"https://doi.org/arxiv-2404.18761","url":null,"abstract":"This paper develops a new dual approach to compute the hedging portfolio of a\u0000Bermudan option and its initial value. It gives a \"purely dual\" algorithm\u0000following the spirit of Rogers (2010) in the sense that it only relies on the\u0000dual pricing formula. The key is to rewrite the dual formula as an excess\u0000reward representation and to combine it with a strict convexification\u0000technique. The hedging strategy is then obtained by using a Monte Carlo method,\u0000solving backward a sequence of least square problems. We show convergence\u0000results for our algorithm and test it on many different Bermudan options.\u0000Beyond giving directly the hedging portfolio, the strength of the algorithm is\u0000to assess both the relevance of including financial instruments in the hedging\u0000portfolio and the effect of the rebalancing frequency.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140828417","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
Mean Field Game of High-Frequency Anticipatory Trading 高频预期交易的均势博弈
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-04-28 DOI: arxiv-2404.18200
Xue Cheng, Meng Wang, Ziyi Xu
{"title":"Mean Field Game of High-Frequency Anticipatory Trading","authors":"Xue Cheng, Meng Wang, Ziyi Xu","doi":"arxiv-2404.18200","DOIUrl":"https://doi.org/arxiv-2404.18200","url":null,"abstract":"The interactions between a large population of high-frequency traders (HFTs)\u0000and a large trader (LT) who executes a certain amount of assets at discrete\u0000time points are studied. HFTs are faster in the sense that they trade\u0000continuously and predict the transactions of LT. A jump process is applied to\u0000model the transition of HFTs' attitudes towards inventories and the equilibrium\u0000is solved through the mean field game approach. When the crowd of HFTs is\u0000averse to running (ending) inventories, they first take then supply liquidity\u0000at each transaction of LT (throughout the whole execution period).\u0000Inventory-averse HFTs lower LT's costs if the market temporary impact is\u0000relatively large to the permanent one. What's more, the repeated liquidity\u0000consuming-supplying behavior of HFTs makes LT's optimal strategy close to\u0000uniform trading.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140828407","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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