Mathematical Finance最新文献

{"title":"Hedging of Fixing Exposure","authors":"Johannes Muhle-Karbe,&nbsp;Roel Oomen,&nbsp;Benjamin Weber","doi":"10.1111/mafi.12464","DOIUrl":"https://doi.org/10.1111/mafi.12464","url":null,"abstract":"<p>FX fixings are an indispensable and widely used reference rate in a market that trades continuously without an official close. Yet, a dealer's handling of fix transactions is a much debated topic. Especially when exposure to the fix is large relative to available market liquidity and hedging may extend to the pre-fix window, an inherent conflict of interest can arise between dealer and client. In this paper we use a model with permanent and transient market impact to characterize a dealer's optimal strategy to hedge fixing exposure. We show that smaller fix exposures are fully hedged over the calculation window, but that larger fix transactions are optimally hedged over a longer horizon that includes the pre-fix window. A client's all-in transaction costs can be lowered by pre-fix hedging provided that transient impact decays sufficiently quickly and dominates permanent impact.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"35 4","pages":"818-840"},"PeriodicalIF":2.4,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12464","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145057914","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}

{"title":"Optimal Liquidation With Signals: The General Propagator Case","authors":"Eduardo Abi Jaber,&nbsp;Eyal Neuman","doi":"10.1111/mafi.12465","DOIUrl":"https://doi.org/10.1111/mafi.12465","url":null,"abstract":"<p>We consider a class of optimal liquidation problems where the agent's transactions create transient price impact driven by a Volterra-type propagator along with temporary price impact. We formulate these problems as maximization of a revenue-risk functionals, where the agent also exploits available information on a progressively measurable price predicting signal. By using an infinite dimensional stochastic control approach, we characterize the value function in terms of a solution to a free-boundary <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$L^2$</annotation>\u0000 </semantics></math>-valued backward stochastic differential equation and an operator-valued Riccati equation. We then derive analytic solutions to these equations, which yields an explicit expression for the optimal trading strategy. We show that our formulas can be implemented in a straightforward and efficient way for a large class of price impact kernels with possible singularities such as the power-law kernel.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"35 4","pages":"841-866"},"PeriodicalIF":2.4,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12465","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145058083","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}

{"title":"Volatility Models in Practice: Rough, Path-Dependent, or Markovian?","authors":"Eduardo Abi Jaber,&nbsp;Shaun (Xiaoyuan) Li","doi":"10.1111/mafi.12463","DOIUrl":"https://doi.org/10.1111/mafi.12463","url":null,"abstract":"<div>\u0000 \u0000 <p>We present an empirical study examining several claims related to option prices in rough volatility literature using SPX options data. Our results show that rough volatility models with the parameter <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 <mo>∈</mo>\u0000 <mo>(</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$H in (0,1/2)$</annotation>\u0000 </semantics></math> are inconsistent with the global shape of SPX smiles. In particular, the at-the-money SPX skew is incompatible with the power-law shape generated by these models, which increases too fast for short maturities and decays too slowly for longer maturities. For maturities between 1 week and 3 months, rough volatility models underperform one-factor Markovian models with the same number of parameters. When extended to longer maturities, rough volatility models do not consistently outperform one-factor Markovian models. Our study identifies a non-rough path-dependent model and a two-factor Markovian model that outperform their rough counterparts in capturing SPX smiles between 1 week and 3 years, with only three to four parameters.</p></div>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"35 4","pages":"796-817"},"PeriodicalIF":2.4,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145057916","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}

{"title":"Optimal Contracts for Delegated Order Execution","authors":"Martin Larsson,&nbsp;Johannes Muhle-Karbe,&nbsp;Benjamin Weber","doi":"10.1111/mafi.12462","DOIUrl":"https://doi.org/10.1111/mafi.12462","url":null,"abstract":"<p>We determine the optimal affine contract for a client who delegates their order execution to a dealer. Existence and uniqueness are established for general linear price impact dynamics of the dealer's trades. Explicit solutions are available for the model of Obizhaeva and Wang, for example, and a simple gradient descent algorithm is applicable in general. The optimal contract allows the client to almost achieve the first-best performance without any agency conflicts for many reasonable parameter values. Common trading arrangements arise as limiting cases. In particular, optimal contracts for many reasonable model parameters resemble the “fixing contract” common in FX markets, in that they only incorporate market prices briefly before the conclusion of the trade. Price manipulation by the dealer is avoided by only putting a sufficiently small weight on these prices, and complementing this part of the contract with a sufficiently large fixed fee.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"35 4","pages":"779-795"},"PeriodicalIF":2.4,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12462","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145058043","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}

{"title":"Statistical Error Bounds for Weighted Mean and Median With Application to Robust Aggregation of Cryptocurrency Data","authors":"Michaël Allouche,&nbsp;Mnacho Echenim,&nbsp;Emmanuel Gobet,&nbsp;Anne-Claire Maurice","doi":"10.1111/mafi.12461","DOIUrl":"https://doi.org/10.1111/mafi.12461","url":null,"abstract":"<div>\u0000 \u0000 <p>We study price aggregation methodologies applied to crypto-currency prices with quotations fragmented on different platforms. An intrinsic difficulty is that the price returns and volumes are heavy-tailed, with many outliers, making averaging and aggregation challenging. While conventional methods rely on volume-weighted average prices (called VWAPs), or volume-weighted median prices (called VWMs), we develop a new robust weighted median (RWM) estimator that is robust to price and volume outliers. Our study is based on new probabilistic concentration inequalities for weighted means and weighted quantiles under different tail assumptions (heavy tails, sub-gamma tails, sub-Gaussian tails). This justifies that fluctuations of VWAP and VWM are statistically important given the heavy-tailed properties of volumes and/or prices. We show that our RWM estimator overcomes this problem and also satisfies all the desirable properties of a price aggregator. We illustrate the behavior of RWM on synthetic data (within a parametric model close to real data): Our estimator achieves a statistical accuracy twice as good as its competitors, and also allows to recover realized volatilities in a very accurate way. Tests on real data are also performed and confirm the good behavior of the estimator on various use cases.</p></div>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"35 4","pages":"760-778"},"PeriodicalIF":2.4,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145057886","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}

{"title":"A Pure Dual Approach for Hedging Bermudan Options","authors":"Aurélien Alfonsi,&nbsp;Ahmed Kebaier,&nbsp;Jérôme Lelong","doi":"10.1111/mafi.12460","DOIUrl":"https://doi.org/10.1111/mafi.12460","url":null,"abstract":"<p>This paper develops a new dual approach to compute the hedging portfolio of a Bermudan option and its initial value. It gives a “purely dual” algorithm following the spirit of Rogers in the sense that it only relies on the dual pricing formula. The key is to rewrite the dual formula as an excess reward representation and to combine it with a strict convexification technique. The hedging strategy is then obtained by using a Monte-Carlo method, solving backward a sequence of least square problems. We show convergence results for our algorithm and test it on many different Bermudan options. Beyond giving directly the hedging portfolio, the strength of the algorithm is to assess both the relevance of including financial instruments in the hedging portfolio and the effect of the rebalancing frequency.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"35 4","pages":"745-759"},"PeriodicalIF":2.4,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12460","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145057875","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}

{"title":"Systemic Robustness: A Mean-Field Particle System Approach","authors":"Erhan Bayraktar,&nbsp;Gaoyue Guo,&nbsp;Wenpin Tang,&nbsp;Yuming Paul Zhang","doi":"10.1111/mafi.12459","DOIUrl":"https://doi.org/10.1111/mafi.12459","url":null,"abstract":"<p>This paper is concerned with the problem of capital provision in a large particle system modeled by stochastic differential equations involving hitting times, which arises from considerations of systemic risk in a financial network. Motivated by Tang and Tsai, we focus on the number or proportion of surviving entities that never default to measure the systemic robustness. First we show that the mean-field particle system and its limit McKean–Vlasov equation are both well-posed by virtue of the notion of minimal solutions. We then establish a connection between the proportion of surviving entities in the large particle system and the probability of default in the McKean–Vlasov equation as the size of the interacting particle system <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$N$</annotation>\u0000 </semantics></math> tends to infinity. Finally, we study the asymptotic efficiency of capital provision for different drift <span></span><math>\u0000 <semantics>\u0000 <mi>β</mi>\u0000 <annotation>$beta$</annotation>\u0000 </semantics></math>, which is linked to the economy regime: The expected number of surviving entities has a uniform upper bound if <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>β</mi>\u0000 <mo>&lt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$beta &lt;0$</annotation>\u0000 </semantics></math>; it is of order <span></span><math>\u0000 <semantics>\u0000 <msqrt>\u0000 <mi>N</mi>\u0000 </msqrt>\u0000 <annotation>$sqrt {N}$</annotation>\u0000 </semantics></math> if <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>β</mi>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$beta =0$</annotation>\u0000 </semantics></math>; and it is of order <span></span><math>\u0000 <semantics>\u0000 <mi>N</mi>\u0000 <annotation>$N$</annotation>\u0000 </semantics></math> if <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>β</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$beta &gt;0$</annotation>\u0000 </semantics></math>, where the effect of capital provision is negligible.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"35 4","pages":"727-744"},"PeriodicalIF":2.4,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12459","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145058060","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}

{"title":"Polar Coordinates for the 3/2 Stochastic Volatility Model","authors":"Paul Nekoranik","doi":"10.1111/mafi.12455","DOIUrl":"https://doi.org/10.1111/mafi.12455","url":null,"abstract":"&lt;p&gt;The 3/2 stochastic volatility model is a continuous positive process &lt;i&gt;s&lt;/i&gt; with a correlated infinitesimal variance process &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;ν&lt;/mi&gt;\u0000 &lt;annotation&gt;$nu $&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. The exact definition is provided in the Introduction immediately below. By inspecting the geometry associated with this model, we discover an explicit smooth map &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;ψ&lt;/mi&gt;\u0000 &lt;annotation&gt;$ psi $&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; from &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$({mathbb{R}}^+)^2 $&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; to the punctured plane &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${mathbb{R}}^2-(0,0)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; for which the process &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;v&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;ψ&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;ν&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(u,v)=psi(nu,s)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; satisfies an SDE of a simpler form, with independent Brownian motions and the identity matrix as diffusion coefficient. Moreover, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ν&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(nu_t,s_t)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is r","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"35 3","pages":"708-723"},"PeriodicalIF":1.6,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12455","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144524683","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}

{"title":"Spanning Multi-Asset Payoffs With ReLUs","authors":"Sébastien Bossu,&nbsp;Stéphane Crépey,&nbsp;Hoang-Dung Nguyen","doi":"10.1111/mafi.12454","DOIUrl":"https://doi.org/10.1111/mafi.12454","url":null,"abstract":"<p>We propose a distributional formulation of the spanning problem of a multi-asset payoff by vanilla basket options. This problem is shown to have a unique solution if and only if the payoff function is even and absolutely homogeneous, and we establish a Fourier-based formula to calculate the solution. Financial payoffs are typically piecewise linear, resulting in a solution that may be derived explicitly, yet may also be hard to exploit numerically. One-hidden-layer feedforward neural networks instead provide a natural and efficient numerical alternative for discrete spanning. We test this approach for a selection of archetypal payoffs and obtain better hedging results with vanilla basket options compared to industry-favored approaches based on single-asset vanilla hedges.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"35 3","pages":"682-707"},"PeriodicalIF":1.6,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12454","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144524795","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}

{"title":"Rough PDEs for Local Stochastic Volatility Models","authors":"Peter Bank,&nbsp;Christian Bayer,&nbsp;Peter K. Friz,&nbsp;Luca Pelizzari","doi":"10.1111/mafi.12458","DOIUrl":"https://doi.org/10.1111/mafi.12458","url":null,"abstract":"<p>In this work, we introduce a novel pricing methodology in general, possibly non-Markovian local stochastic volatility (LSV) models. We observe that by conditioning the LSV dynamics on the Brownian motion that drives the volatility, one obtains a time-inhomogeneous Markov process. Using tools from rough path theory, we describe how to precisely understand the conditional LSV dynamics and reveal their Markovian nature. The latter allows us to connect the conditional dynamics to so-called rough partial differential equations (RPDEs), through a Feynman–Kac type of formula. In terms of European pricing, conditional on realizations of one Brownian motion, we can compute conditional option prices by solving the corresponding linear RPDEs, and then average over all samples to find unconditional prices. Our approach depends only minimally on the specification of the volatility, making it applicable for a wide range of classical and rough LSV models, and it establishes a PDE pricing method for non-Markovian models. Finally, we present a first glimpse at numerical methods for RPDEs and apply them to price European options in several rough LSV models.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"35 3","pages":"661-681"},"PeriodicalIF":1.6,"publicationDate":"2025-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12458","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144524777","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}