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Recursive Optimal Stopping with Poisson Stopping Constraints 具有泊松停机约束条件的递归优化停机
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-07-25 DOI: arxiv-2407.17975
Gechun Liang, Wei Wei, Zhen Wu, Zhenda Xu
{"title":"Recursive Optimal Stopping with Poisson Stopping Constraints","authors":"Gechun Liang, Wei Wei, Zhen Wu, Zhenda Xu","doi":"arxiv-2407.17975","DOIUrl":"https://doi.org/arxiv-2407.17975","url":null,"abstract":"This paper solves a recursive optimal stopping problem with Poisson stopping\u0000constraints using the penalized backward stochastic differential equation\u0000(PBSDE) with jumps. Stopping in this problem is only allowed at Poisson random\u0000intervention times, and jumps play a significant role not only through the\u0000stopping times but also in the recursive objective functional and model\u0000coefficients. To solve the problem, we propose a decomposition method based on\u0000Jacod-Pham that allows us to separate the problem into a series of sub-problems\u0000between each pair of consecutive Poisson stopping times. To represent the value\u0000function of the recursive optimal stopping problem when the initial time falls\u0000between two consecutive Poisson stopping times and the generator is\u0000concave/convex, we leverage the comparison theorem of BSDEs with jumps. We then\u0000apply the representation result to American option pricing in a nonlinear\u0000market with Poisson stopping constraints.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"352 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141777902","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
Market Making with Exogenous Competition 外生竞争下的做市商
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-07-24 DOI: arxiv-2407.17393
Robert Boyce, Martin Herdegen, Leandro Sánchez-Betancourt
{"title":"Market Making with Exogenous Competition","authors":"Robert Boyce, Martin Herdegen, Leandro Sánchez-Betancourt","doi":"arxiv-2407.17393","DOIUrl":"https://doi.org/arxiv-2407.17393","url":null,"abstract":"We study liquidity provision in the presence of exogenous competition. We\u0000consider a `reference market maker' who monitors her inventory and the\u0000aggregated inventory of the competing market makers. We assume that the\u0000competing market makers use a `rule of thumb' to determine their posted depths,\u0000depending linearly on their inventory. By contrast, the reference market maker\u0000optimises over her posted depths, and we assume that her fill probability\u0000depends on the difference between her posted depths and the competition's\u0000depths in an exponential way. For a linear-quadratic goal functional, we show\u0000that this model admits an approximate closed-form solution. We illustrate the\u0000features of our model and compare against alternative ways of solving the\u0000problem either via an Euler scheme or state-of-the-art reinforcement learning\u0000techniques.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141777900","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
Equilibrium control theory for Kihlstrom-Mirman preferences in continuous time 基尔斯特罗姆-米尔曼连续时间偏好的均衡控制理论
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-07-23 DOI: arxiv-2407.16525
Luca De Gennaro Aquino, Sascha Desmettre, Yevhen Havrylenko, Mogens Steffensen
{"title":"Equilibrium control theory for Kihlstrom-Mirman preferences in continuous time","authors":"Luca De Gennaro Aquino, Sascha Desmettre, Yevhen Havrylenko, Mogens Steffensen","doi":"arxiv-2407.16525","DOIUrl":"https://doi.org/arxiv-2407.16525","url":null,"abstract":"In intertemporal settings, the multiattribute utility theory of Kihlstrom and\u0000Mirman suggests the application of a concave transform of the lifetime utility\u0000index. This construction, while allowing time and risk attitudes to be\u0000separated, leads to dynamically inconsistent preferences. We address this issue\u0000in a game-theoretic sense by formalizing an equilibrium control theory for\u0000continuous-time Markov processes. In these terms, we describe the equilibrium\u0000strategy and value function as the solution of an extended\u0000Hamilton-Jacobi-Bellman system of partial differential equations. We verify\u0000that (the solution of) this system is a sufficient condition for an equilibrium\u0000and examine some of its novel features. A consumption-investment problem for an\u0000agent with CRRA-CES utility showcases our approach.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141777901","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
Weak convergence implies convergence in mean within GGC 弱趋同意味着 GGC 内部平均值趋同
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-07-21 DOI: arxiv-2407.15105
Hasanjan Sayit
{"title":"Weak convergence implies convergence in mean within GGC","authors":"Hasanjan Sayit","doi":"arxiv-2407.15105","DOIUrl":"https://doi.org/arxiv-2407.15105","url":null,"abstract":"We prove that weak convergence within generalized gamma convolution (GGC)\u0000distributions implies convergence in the mean value. We use this fact to show\u0000the robustness of the expected utility maximizing optimal portfolio under\u0000exponential utility function when return vectors are modelled by hyperbolic\u0000distributions.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141777903","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
An Integral Equation Approach for the Valuation of Finite-maturity margin-call Stock Loans 有限期限追加保证金股票贷款估值的积分方程法
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-07-20 DOI: arxiv-2407.14728
Minh-Quan Nguyen, Nhat-Tan Le, Khuong Nguyen-An, Duc-Thi Luu
{"title":"An Integral Equation Approach for the Valuation of Finite-maturity margin-call Stock Loans","authors":"Minh-Quan Nguyen, Nhat-Tan Le, Khuong Nguyen-An, Duc-Thi Luu","doi":"arxiv-2407.14728","DOIUrl":"https://doi.org/arxiv-2407.14728","url":null,"abstract":"This paper examines the pricing issue of margin-call stock loans with finite\u0000maturities under the Black-Scholes-Merton framework. In particular, using a\u0000Fourier Sine transform method, we reduce the partial differential equation\u0000governing the price of a margin-call stock loan into an ordinary differential\u0000equation, the solution of which can be easily found (in the Fourier Sine space)\u0000and analytically inverted into the original space. As a result, we obtain an\u0000integral representation of the value of the stock loan in terms of the unknown\u0000optimal exit prices, which are, in turn, governed by a Volterra integral\u0000equation. We thus can break the pricing problem of margin-call stock loans into\u0000two steps: 1) finding the optimal exit prices by solving numerically the\u0000governing Volterra integral equation and 2) calculating the values of\u0000margin-call stock loans based on the obtained optimal exit prices. By\u0000validating and comparing with other available numerical methods, we show that\u0000our proposed numerical scheme offers a reliable and efficient way to calculate\u0000the service fee of a margin-call stock loan contract, track the contract value\u0000over time, and compute the level of stock price above which it is optimal to\u0000exit the contract. The effects of the margin-call feature on the loan contract\u0000are also examined and quantified.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141777905","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
Unified Asymptotics For Investment Under Illiquidity: Transaction Costs And Search Frictions 流动性不足下投资的统一渐近论：交易成本与搜索摩擦
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-07-18 DOI: arxiv-2407.13547
Tae Ung Gang, Jin Hyuk Choi
{"title":"Unified Asymptotics For Investment Under Illiquidity: Transaction Costs And Search Frictions","authors":"Tae Ung Gang, Jin Hyuk Choi","doi":"arxiv-2407.13547","DOIUrl":"https://doi.org/arxiv-2407.13547","url":null,"abstract":"This paper investigates the optimal investment problem in a market with two\u0000types of illiquidity: transaction costs and search frictions. Extending the\u0000framework established by arXiv:2101.09936, we analyze a power-utility\u0000maximization problem where an investor encounters proportional transaction\u0000costs and trades only when a Poisson process triggers trading opportunities. We\u0000show that the optimal trading strategy is described by a no-trade region. We\u0000introduce a novel asymptotic framework applicable when both transaction costs\u0000and search frictions are small. Using this framework, we derive explicit\u0000asymptotics for the no-trade region and the value function along a specific\u0000parametric curve. This approach unifies existing asymptotic results for models\u0000dealing exclusively with either transaction costs or search frictions.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"245 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141738918","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 Mean Field Game approach for pollution regulation of competitive firms 竞争性企业污染监管的均场博弈方法
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-07-17 DOI: arxiv-2407.12754
Gianmarco Del Sarto, Marta Leocata, Giulia Livieri
{"title":"A Mean Field Game approach for pollution regulation of competitive firms","authors":"Gianmarco Del Sarto, Marta Leocata, Giulia Livieri","doi":"arxiv-2407.12754","DOIUrl":"https://doi.org/arxiv-2407.12754","url":null,"abstract":"We develop a model based on mean-field games of competitive firms producing\u0000similar goods according to a standard AK model with a depreciation rate of\u0000capital generating pollution as a byproduct. Our analysis focuses on the\u0000widely-used cap-and-trade pollution regulation. Under this regulation, firms\u0000have the flexibility to respond by implementing pollution abatement, reducing\u0000output, and participating in emission trading, while a regulator dynamically\u0000allocates emission allowances to each firm. The resulting mean-field game is of\u0000linear quadratic type and equivalent to a mean-field type control problem,\u0000i.e., it is a potential game. We find explicit solutions to this problem\u0000through the solutions to differential equations of Riccati type. Further, we\u0000investigate the carbon emission equilibrium price that satisfies the market\u0000clearing condition and find a specific form of FBSDE of McKean-Vlasov type with\u0000common noise. The solution to this equation provides an approximate equilibrium\u0000price. Additionally, we demonstrate that the degree of competition is vital in\u0000determining the economic consequences of pollution regulation.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141738944","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-Variance Optimization for Participating Life Insurance Contracts 分红人寿保险合同的均值-方差优化
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-07-16 DOI: arxiv-2407.11761
Felix Fießinger, Mitja Stadje
{"title":"Mean-Variance Optimization for Participating Life Insurance Contracts","authors":"Felix Fießinger, Mitja Stadje","doi":"arxiv-2407.11761","DOIUrl":"https://doi.org/arxiv-2407.11761","url":null,"abstract":"This paper studies the equity holders' mean-variance optimal portfolio choice\u0000problem for (non-)protected participating life insurance contracts. We derive\u0000explicit formulas for the optimal terminal wealth and the optimal strategy in\u0000the multi-dimensional Black-Scholes model, showing the existence of all\u0000necessary parameters. In incomplete markets, we state Hamilton-Jacobi-Bellman\u0000equations for the value function. Moreover, we provide a numerical analysis of\u0000the Black-Scholes market. The equity holders on average increase their\u0000investment into the risky asset in bad economic states and decrease their\u0000investment over time.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141718271","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
Optimal Carbon Emission Control With Allowances Purchasing 通过购买配额优化碳排放控制
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-07-11 DOI: arxiv-2407.08477
Xinfu Chen, Yuchao Dong, Wenlin Huang, Jin Liang
{"title":"Optimal Carbon Emission Control With Allowances Purchasing","authors":"Xinfu Chen, Yuchao Dong, Wenlin Huang, Jin Liang","doi":"arxiv-2407.08477","DOIUrl":"https://doi.org/arxiv-2407.08477","url":null,"abstract":"In this paper, we consider a company can simultaneously reduce its emissions\u0000and buy carbon allowances at any time. We establish an optimal control model\u0000involving two stochastic processes with two control variables, which is a\u0000singular control problem. This model can then be converted into a\u0000Hamilton-Jacobi-Bellman (HJB) equation, which is a two-dimensional variational\u0000equality with gradient barrier, so that the free boundary is a surface. We\u0000prove the existence and uniqueness of the solution. Finally, some numerical\u0000results are shown.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141608742","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
Subleading correction to the Asian options volatility in the Black-Scholes model 布莱克-斯科尔斯模型中亚洲期权波动率的次引导修正
arXiv - QuantFin - Mathematical Finance Pub Date : 2024-07-06 DOI: arxiv-2407.05142
Dan Pirjol
{"title":"Subleading correction to the Asian options volatility in the Black-Scholes model","authors":"Dan Pirjol","doi":"arxiv-2407.05142","DOIUrl":"https://doi.org/arxiv-2407.05142","url":null,"abstract":"The short maturity limit $Tto 0$ for the implied volatility of an Asian\u0000option in the Black-Scholes model is determined by the large deviations\u0000property for the time-average of the geometric Brownian motion. In this note we\u0000derive the subleading $O(T)$ correction to this implied volatility, using an\u0000asymptotic expansion for the Hartman-Watson distribution. The result is used to\u0000compute subleading corrections to Asian options prices in a small maturity\u0000expansion, sharpening the leading order result obtained using large deviations\u0000theory. We demonstrate good numerical agreement with precise benchmarks for\u0000Asian options pricing in the Black-Scholes model.","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141567051","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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