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Smart TWAP Trading in Continuous-Time Equilibria 连续时间均衡中的智能TWAP交易
arXiv: Mathematical Finance Pub Date : 2018-03-22 DOI: 10.2139/ssrn.3146658
J. Choi, Kasper Larsen, Duane J. Seppi
{"title":"Smart TWAP Trading in Continuous-Time Equilibria","authors":"J. Choi, Kasper Larsen, Duane J. Seppi","doi":"10.2139/ssrn.3146658","DOIUrl":"https://doi.org/10.2139/ssrn.3146658","url":null,"abstract":"This paper presents a continuous-time equilibrium model of liquidity provision in a market with multiple strategic investors with intraday trading targets. We show analytically that there are infinitely many Nash equilibria. We solve for the welfare-maximizing equilibrium and the competitive equilibrium, and we illustrate that these equilibria are different. The model is easily computed numerically, and we provide a number of numerical illustrations.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130775645","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: 12
Option Pricing Models Driven by the Space-Time Fractional Diffusion: Series Representation and Applications 时空分数扩散驱动的期权定价模型:序列表示及应用
arXiv: Mathematical Finance Pub Date : 2018-02-27 DOI: 10.3390/fractalfract2010015
Jean-Philippe Aguilar, J. Korbel
{"title":"Option Pricing Models Driven by the Space-Time Fractional Diffusion: Series Representation and Applications","authors":"Jean-Philippe Aguilar, J. Korbel","doi":"10.3390/fractalfract2010015","DOIUrl":"https://doi.org/10.3390/fractalfract2010015","url":null,"abstract":"In this paper, we focus on option pricing models based on space-time fractional diffusion. We briefly revise recent results which show that the option price can be represented in the terms of rapidly converging double-series and apply these results to the data from real markets. We focus on estimation of model parameters from the market data and estimation of implied volatility within the space-time fractional option pricing models.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131226379","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: 13
Arbitrage-Free Regularization 无套利的正则化
arXiv: Mathematical Finance Pub Date : 2017-10-14 DOI: 10.3390/RISKS8020040
Anastasis Kratsios, Cody B. Hyndman
{"title":"Arbitrage-Free Regularization","authors":"Anastasis Kratsios, Cody B. Hyndman","doi":"10.3390/RISKS8020040","DOIUrl":"https://doi.org/10.3390/RISKS8020040","url":null,"abstract":"We introduce an unsupervised and non-anticipative machine learning algorithm which is able to detect and remove arbitrage from a wide variety models. In this framework, fundamental results and techniques from risk-neutral pricing theory such as NFLVR, market completeness, and changes of measure are given an equivalent formulation and extended to models which are deformable into arbitrage-free models. We use this scheme to construct a meta-algorithm which ensures that a wide range of factor estimation schemes return arbitrage-free estimates and incorporate this additional information into their estimation procedure. We show that using our meta-algorithm we are able to produce more accurate estimates of forward-rate curves, specifically at the long-end. The spread between a model and its arbitrage-free regularization is then used to construct a mis-pricing detection or classification algorithm, which is in turn used to develop a pairs trading strategy. Our theory provides a sound theoretical foundation for a risk-neutral pricing theory capable of handling models which potentially admit arbitrage but which can which can be deformed into arbitrage-free models.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131567173","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: 7
Wealth distribution in presence of debts. A Fokker--Planck description 存在债务的财富分配。福克-普朗克描述
arXiv: Mathematical Finance Pub Date : 2017-09-28 DOI: 10.4310/CMS.2018.V16.N2.A11
M. Torregrossa, G. Toscani
{"title":"Wealth distribution in presence of debts. A Fokker--Planck description","authors":"M. Torregrossa, G. Toscani","doi":"10.4310/CMS.2018.V16.N2.A11","DOIUrl":"https://doi.org/10.4310/CMS.2018.V16.N2.A11","url":null,"abstract":"We consider here a Fokker--Planck equation with variable coefficient of diffusion which appears in the modeling of the wealth distribution in a multi-agent society. At difference with previous studies, to describe a society in which agents can have debts, we allow the wealth variable to be negative. It is shown that, even starting with debts, if the initial mean wealth is assumed positive, the solution of the Fokker--Planck equation is such that debts are absorbed in time, and a unique equilibrium density located in the positive part of the real axis will be reached.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125899814","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: 15
Shot-Noise Processes in Finance 金融中的短噪声过程
arXiv: Mathematical Finance Pub Date : 2016-12-20 DOI: 10.1007/978-3-319-50986-0_18
Thorsten Schmidt
{"title":"Shot-Noise Processes in Finance","authors":"Thorsten Schmidt","doi":"10.1007/978-3-319-50986-0_18","DOIUrl":"https://doi.org/10.1007/978-3-319-50986-0_18","url":null,"abstract":"","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116484982","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: 15
Criteria for the Absence and Existence of Arbitrage in Multi-Dimensional Diffusion Markets 多维扩散市场中套利存在与不存在的准则
arXiv: Mathematical Finance Pub Date : 2016-09-06 DOI: 10.1142/S0219024918500024
David Criens
{"title":"Criteria for the Absence and Existence of Arbitrage in Multi-Dimensional Diffusion Markets","authors":"David Criens","doi":"10.1142/S0219024918500024","DOIUrl":"https://doi.org/10.1142/S0219024918500024","url":null,"abstract":"In this article, we study the set of equivalent (local) martingale measures for financial markets driven by multi-dimensional diffusions. We give conditions for the existence of equivalent (local) martingale measures in terms of existence and uniqueness properties of martingale problems. Based on these we derive deterministic criteria for the existence and non-existence of equivalent (local) martingale measures. As an application, we construct a financial market in which the number of risky assets determines the absence of arbitrage and equals the number of sources of risk.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116400711","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: 8
Recursive utility optimization with concave coefficients 凹系数递归效用优化
arXiv: Mathematical Finance Pub Date : 2016-07-03 DOI: 10.3934/MCRF.2018033
Shaolin Ji, Xiaomin Shi
{"title":"Recursive utility optimization with concave coefficients","authors":"Shaolin Ji, Xiaomin Shi","doi":"10.3934/MCRF.2018033","DOIUrl":"https://doi.org/10.3934/MCRF.2018033","url":null,"abstract":"This paper concerns the recursive utility maximization problem. We assume that the coefficients of the wealth equation and the recursive utility are concave. Then some interesting and important cases with nonlinear and nonsmooth coefficients satisfy our assumption. After given an equivalent backward formulation of our problem, we employ the Fenchel-Legendre transform and derive the corresponding variational formulation. By the convex duality method, the primal \"sup-inf\" problem is translated to a dual minimization problem and the saddle point of our problem is derived. Finally, we obtain the optimal terminal wealth. To illustrate our results, three cases for investors with ambiguity aversion are explicitly worked out under some special assumptions.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"114 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124547982","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: 1
On optimal strategies for utility maximizers in the Arbitrage Pricing Model 套利定价模型中效用最大化者的最优策略
arXiv: Mathematical Finance Pub Date : 2016-02-18 DOI: 10.1142/S0219024916500473
M. Rásonyi
{"title":"On optimal strategies for utility maximizers in the Arbitrage Pricing Model","authors":"M. Rásonyi","doi":"10.1142/S0219024916500473","DOIUrl":"https://doi.org/10.1142/S0219024916500473","url":null,"abstract":"We consider a popular model of microeconomics with countably many assets: the Arbitrage Pricing Model. We study the problem of optimal investment under an expected utility criterion and look for conditions ensuring the existence of optimal strategies. Previous results required a certain restrictive hypothesis on the tails of asset return distributions. Using a different method, we manage to remove this hypothesis, at the price of stronger assumptions on the moments of asset returns.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127296491","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: 9
Optimal Control of an Energy Storage Facility Under a Changing Economic Environment and Partial Information 经济环境变化和部分信息条件下储能设施的最优控制
arXiv: Mathematical Finance Pub Date : 2016-02-15 DOI: 10.1142/S0219024916500266
Anton A. Shardin, Michaela Szolgyenyi
{"title":"Optimal Control of an Energy Storage Facility Under a Changing Economic Environment and Partial Information","authors":"Anton A. Shardin, Michaela Szolgyenyi","doi":"10.1142/S0219024916500266","DOIUrl":"https://doi.org/10.1142/S0219024916500266","url":null,"abstract":"In this paper we consider an energy storage optimization problem in finite time in a model with partial information that allows for a changing economic environment. The state process consists of the storage level controlled by the storage manager and the energy price process, which is a diffusion process the drift of which is assumed to be unobservable. We apply filtering theory to find an alternative state process which is adapted to our observation filtration. For this alternative state process we derive the associated Hamilton-Jacobi-Bellman equation and solve the optimization problem numerically. This results in a candidate for the optimal policy for which it is a-priori not clear whether the controlled state process exists. Hence, we prove an existence and uniqueness result for a class of time-inhomogeneous stochastic differential equations with discontinuous drift and singular diffusion coefficient. Finally, we apply our result to prove admissibility of the candidate optimal control.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132138416","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: 21
A unified view of LIBOR models LIBOR模型的统一视图
arXiv: Mathematical Finance Pub Date : 2016-01-06 DOI: 10.1007/978-3-319-45875-5_18
K. Glau, Z. Grbac, A. Papapantoleon
{"title":"A unified view of LIBOR models","authors":"K. Glau, Z. Grbac, A. Papapantoleon","doi":"10.1007/978-3-319-45875-5_18","DOIUrl":"https://doi.org/10.1007/978-3-319-45875-5_18","url":null,"abstract":"","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131103694","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: 5
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