Mathematical Finance最新文献_第5页

Epstein-Zin utility maximization on a random horizon 随机视野中的Epstein‐Zin效用最大化

IF 1.6 3区经济学

Mathematical Finance Pub Date : 2023-06-01 DOI: 10.1111/mafi.12404

Joshua Aurand, Yu-Jui Huang

引用次数: 5

Dynamics of market making algorithms in dealer markets: Learning and tacit collusion 交易商市场中做市算法的动态:学习与隐性串谋

IF 1.6 3区经济学

Mathematical Finance Pub Date : 2023-05-30 DOI: 10.1111/mafi.12401

Rama Cont, Wei Xiong

引用次数: 0

Trading under the proof-of-stake protocol – A continuous-time control approach 在权益证明协议下进行交易-一种连续时间控制方法

IF 1.6 3区经济学

Mathematical Finance Pub Date : 2023-05-24 DOI: 10.1111/mafi.12403

Wenpin Tang, David D. Yao

{"title":"Trading under the proof-of-stake protocol – A continuous-time control approach","authors":"Wenpin Tang, David D. Yao","doi":"10.1111/mafi.12403","DOIUrl":"10.1111/mafi.12403","url":null,"abstract":"We develop a continuous-time control approach to optimal trading in a Proof-of-Stake (PoS) blockchain, formulated as a consumption-investment problem that aims to strike the optimal balance between a participant's (or agent's) utility from holding/trading stakes and utility from consumption. We present solutions via dynamic programming and the Hamilton–Jacobi–Bellman (HJB) equations. When the utility functions are linear or convex, we derive close-form solutions and show that the bang-bang strategy is optimal (i.e., always buy or sell at full capacity). Furthermore, we bring out the explicit connection between the rate of return in trading/holding stakes and the participant's risk-adjusted valuation of the stakes. In particular, we show when a participant is risk-neutral or risk-seeking, corresponding to the risk-adjusted valuation being a martingale or a sub-martingale, the optimal strategy must be to either buy all the time, sell all the time, or first buy then sell, and with both buying and selling executed at full capacity. We also propose a risk-control version of the consumption-investment problem; and for a special case, the “stake-parity” problem, we show a mean-reverting strategy is optimal.","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44081069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Local volatility under rough volatility 粗波动下的局部波动

IF 1.6 3区经济学

Mathematical Finance Pub Date : 2023-05-24 DOI: 10.1111/mafi.12392

Florian Bourgey, Stefano De Marco, Peter K. Friz, Paolo Pigato

{"title":"Local volatility under rough volatility","authors":"Florian Bourgey, Stefano De Marco, Peter K. Friz, Paolo Pigato","doi":"10.1111/mafi.12392","DOIUrl":"10.1111/mafi.12392","url":null,"abstract":"Several asymptotic results for the implied volatility generated by a rough volatility model have been obtained in recent years (notably in the small-maturity regime), providing a better understanding of the shapes of the volatility surface induced by rough volatility models, supporting their calibration power to SP500 option data. Rough volatility models also generate a local volatility surface, via the so-called Markovian projection of the stochastic volatility. We complement the existing results on implied volatility by studying the asymptotic behavior of the local volatility surface generated by a class of rough stochastic volatility models, encompassing the rough Bergomi model. Notably, we observe that the celebrated “1/2 skew rule” linking the short-term at-the-money skew of the implied volatility to the short-term at-the-money skew of the local volatility, a consequence of the celebrated “harmonic mean formula” of [Berestycki et al. (2002). Quantitative Finance, 2, 61–69], is replaced by a new rule: the ratio of the at-the-money implied and local volatility skews tends to the constant <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mo>(</mo>\u0000 <mi>H</mi>\u0000 <mo>+</mo>\u0000 <mn>3</mn>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$1/(H + 3/2)$</annotation>\u0000 </semantics></math> (as opposed to the constant 1/2), where H is the regularity index of the underlying instantaneous volatility process.","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46921786","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Proximity with affinity: How M&A top executives could exacerbate agency conflicts? 接近与亲和:并购高管如何加剧代理冲突?

IF 1.6 3区经济学

Mathematical Finance Pub Date : 2023-05-17 DOI: 10.3917/fina.pr.023

Jean-Gabriel Cousin, Marion Dupire, Jean-Yves Filbien

引用次数: 0

Asymptotic subadditivity/superadditivity of Value-at-Risk under tail dependence 尾相关下风险值的渐近子可加性/超可加性

IF 1.6 3区经济学

Mathematical Finance Pub Date : 2023-05-15 DOI: 10.1111/mafi.12393

Wenhao Zhu, Lujun Li, Jingping Yang, Jiehua Xie, Liulei Sun

引用次数: 0

The log-moment formula for implied volatility 隐含波动率的对数矩公式

IF 1.6 3区经济学

Mathematical Finance Pub Date : 2023-05-11 DOI: 10.1111/mafi.12396

Vimal Raval, Antoine Jacquier

{"title":"The log-moment formula for implied volatility","authors":"Vimal Raval, Antoine Jacquier","doi":"10.1111/mafi.12396","DOIUrl":"https://doi.org/10.1111/mafi.12396","url":null,"abstract":"We revisit the foundational Moment Formula proved by Roger Lee fifteen years ago. We show that in the absence of arbitrage, if the underlying stock price at time T admits finite log-moments <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>E</mi>\u0000 <mo>[</mo>\u0000 <mo>|</mo>\u0000 <mi>log</mi>\u0000 <msub>\u0000 <mi>S</mi>\u0000 <mi>T</mi>\u0000 </msub>\u0000 <msup>\u0000 <mo>|</mo>\u0000 <mi>q</mi>\u0000 </msup>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>$mathbb {E}[|log S_T|^q]$</annotation>\u0000 </semantics></math> for some positive q, the arbitrage-free growth in the left wing of the implied volatility smile for T is less constrained than Lee's bound. The result is rationalized by a market trading discretely monitored variance swaps wherein the payoff is a function of squared log-returns, and requires no assumption for the underlying price to admit any negative moment. In this respect, the result can be derived from a model-independent setup. As a byproduct, we relax the moment assumptions on the stock price to provide a new proof of the notorious Gatheral–Fukasawa formula expressing variance swaps in terms of the implied volatility.","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12396","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50129610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

A Leland model for delta hedging in central risk books 中央风险账簿中delta套期保值的Leland模型

IF 1.6 3区经济学

Mathematical Finance Pub Date : 2023-05-11 DOI: 10.1111/mafi.12395

Johannes Muhle-Karbe, Zexin Wang, Kevin Webster

{"title":"A Leland model for delta hedging in central risk books","authors":"Johannes Muhle-Karbe, Zexin Wang, Kevin Webster","doi":"10.1111/mafi.12395","DOIUrl":"10.1111/mafi.12395","url":null,"abstract":"Using a tractable extension of the model of Leland (1985), we study how a delta-hedging strategy can realistically be implemented using market and limit orders in a centralized, automated market-making desk that integrates trading and liquidity provision for both options and their underlyings. In the continuous-time limit, the optimal limit-order exposure can be computed explicitly by a pointwise maximization. It is determined by the relative magnitudes of adverse selection, bid–ask spreads, and volatilities. The corresponding option price—from which the option can be replicated using market and limit orders—is characterized via a nonlinear PDE. Our results highlight the benefit of tactical liquidity provision for contrarian trading strategies, even for a trading desk that is not a competitive market maker. More generally, the paper also showcases how reduced-form models are competitive with “brute force” numerical approaches to market microstructure. Both the estimation of microstructure parameters and the simulation of the optimal trading strategy are made concrete and reconciled with real-life high frequency data.","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12395","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43718101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Equilibrium investment with random risk aversion 具有随机风险规避的均衡投资

IF 1.6 3区经济学

Mathematical Finance Pub Date : 2023-05-03 DOI: 10.1111/mafi.12394

Sascha Desmettre, Mogens Steffensen

引用次数: 1

Weak equilibria for time-inconsistent control: With applications to investment-withdrawal decisions 时间不一致控制的弱均衡：在投资退出决策中的应用

IF 1.6 3区经济学

Mathematical Finance Pub Date : 2023-04-29 DOI: 10.1111/mafi.12391

Zongxia Liang, Fengyi Yuan

{"title":"Weak equilibria for time-inconsistent control: With applications to investment-withdrawal decisions","authors":"Zongxia Liang, Fengyi Yuan","doi":"10.1111/mafi.12391","DOIUrl":"10.1111/mafi.12391","url":null,"abstract":"This paper considers time-inconsistent problems when control and stopping strategies are required to be made simultaneously (called stopping control problems by us). We first formulate the time-inconsistent stopping control problems under general multidimensional controlled diffusion model and propose a formal definition of their equilibria. We show that an admissible pair <math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mover>\u0000 <mi>u</mi>\u0000 <mo>̂</mo>\u0000 </mover>\u0000 <mo>,</mo>\u0000 <mi>C</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(hat{u},C)$</annotation>\u0000 </semantics></math> of control-stopping policy is equilibrium if and only if the auxiliary function associated with it solves the extended HJB system, providing a methodology to verify or exclude equilibrium solutions. We provide several examples to illustrate applications to mathematical finance and control theory. For a problem whose reward function endogenously depends on the current wealth, the equilibrium is explicitly obtained. For another model with a nonexponential discount, we prove that any constant proportion strategy can not be equilibrium. We further show that general nonconstant equilibrium exists and is described by singular boundary value problems. This example shows that considering our combined problems is essentially different from investigating them separately. In the end, we also provide a two-dimensional example with a hyperbolic discount.","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43800406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0