Mathematical Finance最新文献

{"title":"Stability of the Epstein–Zin problem","authors":"Michael Monoyios,&nbsp;Oleksii Mostovyi","doi":"10.1111/mafi.12434","DOIUrl":"10.1111/mafi.12434","url":null,"abstract":"<p>We investigate the stability of the Epstein–Zin problem with respect to small distortions in the dynamics of the traded securities. We work in incomplete market model settings, where our parametrization of perturbations allows for joint distortions in returns and volatility of the risky assets and the interest rate. Considering empirically the most relevant specifications of risk aversion and elasticity of intertemporal substitution, we provide a condition that guarantees the convexity of the domain of the underlying problem and results in the existence and uniqueness of a solution to it. Then, we prove the convergence of the optimal consumption streams, the associated wealth processes, the indirect utility processes, and the value functions in the limit when the model perturbations vanish.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"34 4","pages":"1263-1290"},"PeriodicalIF":1.6,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141146340","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":"Put–Call Parities, absence of arbitrage opportunities, and nonlinear pricing rules","authors":"Lorenzo Bastianello,&nbsp;Alain Chateauneuf,&nbsp;Bernard Cornet","doi":"10.1111/mafi.12433","DOIUrl":"10.1111/mafi.12433","url":null,"abstract":"<p>When prices of assets traded in a financial market are determined by nonlinear pricing rules, different parities between call and put options have been considered. We show that, under monotonicity, parities between call and put options and discount certificates characterize ambiguity-sensitive (Choquet and/or Šipoš) pricing rules, that is, pricing rules that can be represented via discounted expectations with respect to non-additive probability measures. We analyze how nonadditivity relates to arbitrage opportunities and we give necessary and sufficient conditions for Choquet and Šipoš pricing rules to be arbitrage free. Finally, we identify violations of the Call-Put Parity with the presence of bid–ask spreads.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"34 4","pages":"1242-1262"},"PeriodicalIF":1.6,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12433","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140301553","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":"The rough Hawkes Heston stochastic volatility model","authors":"Alessandro Bondi,&nbsp;Sergio Pulido,&nbsp;Simone Scotti","doi":"10.1111/mafi.12432","DOIUrl":"10.1111/mafi.12432","url":null,"abstract":"<p>We study an extension of the Heston stochastic volatility model that incorporates rough volatility and jump clustering phenomena. In our model, named the rough Hawkes Heston stochastic volatility model, the spot variance is a rough Hawkes-type process proportional to the intensity process of the jump component appearing in the dynamics of the spot variance itself and the log returns. The model belongs to the class of affine Volterra models. In particular, the Fourier-Laplace transform of the log returns and the square of the volatility index can be computed explicitly in terms of solutions of deterministic Riccati-Volterra equations, which can be efficiently approximated using a multi-factor approximation technique. We calibrate a parsimonious specification of our model characterized by a power kernel and an exponential law for the jumps. We show that our parsimonious setup is able to simultaneously capture, with a high precision, the behavior of the implied volatility smile for both S&amp;P 500 and VIX options. In particular, we observe that in our setting the usual shift in the implied volatility of VIX options is explained by a very low value of the power in the kernel. Our findings demonstrate the relevance, under an affine framework, of rough volatility and self-exciting jumps in order to capture the joint evolution of the S&amp;P 500 and VIX.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"34 4","pages":"1197-1241"},"PeriodicalIF":1.6,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140037372","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":"Special issue on machine learning in finance","authors":"Christa Cuchiero, Ruimeng Hu, Sara Svaluto-Ferro, Renyuan Xu","doi":"10.1111/mafi.12430","DOIUrl":"https://doi.org/10.1111/mafi.12430","url":null,"abstract":"","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"443 ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139841470","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":"Special issue on machine learning in finance","authors":"Christa Cuchiero,&nbsp;Ruimeng Hu,&nbsp;Sara Svaluto-Ferro,&nbsp;Renyuan Xu","doi":"10.1111/mafi.12430","DOIUrl":"10.1111/mafi.12430","url":null,"abstract":"","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"34 2","pages":"259-261"},"PeriodicalIF":1.6,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139781576","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":"Naïve Markowitz policies","authors":"Lin Chen,&nbsp;Xun Yu Zhou","doi":"10.1111/mafi.12431","DOIUrl":"10.1111/mafi.12431","url":null,"abstract":"<p>We study a continuous-time Markowitz mean–variance portfolio selection model in which a naïve agent, unaware of the underlying time-inconsistency, continuously reoptimizes over time. We define the resulting naïve policies through the limit of discretely naïve policies that are committed only in very small time intervals, and derive them analytically and explicitly. We compare naïve policies with pre-committed optimal policies and with consistent planners' equilibrium policies in a Black–Scholes market, and find that the former achieve higher expected terminal returns than originally planned yet are mean–variance inefficient when the risk aversion level is sufficiently small, and always take strictly riskier exposure than equilibrium policies. We finally define an efficiency ratio for comparing return–risk tradeoff with the same original level of risk aversion, and show that naïve policies are always strictly less efficient than pre-committed and equilibrium policies.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"34 4","pages":"1167-1196"},"PeriodicalIF":1.6,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139950003","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":"Mean-field liquidation games with market drop-out","authors":"Guanxing Fu,&nbsp;Paul P. Hager,&nbsp;Ulrich Horst","doi":"10.1111/mafi.12429","DOIUrl":"10.1111/mafi.12429","url":null,"abstract":"<p>We consider a novel class of portfolio liquidation games with market drop-out (“absorption”). More precisely, we consider mean-field and finite player liquidation games where a player drops out of the market when her position hits zero. In particular, round-trips are not admissible. This can be viewed as a no statistical arbitrage condition. In a model with only sellers, we prove that the absorption condition is equivalent to a short selling constraint. We prove that equilibria (both in the mean-field and the finite player game) are given as solutions to a nonlinear higher-order integral equation with endogenous terminal condition. We prove the existence of a unique solution to the integral equation from which we obtain the existence of a unique equilibrium in the MFG and the existence of a unique equilibrium in the <i>N</i>-player game. We establish the convergence of the equilibria in the finite player games to the obtained mean-field equilibrium and illustrate the impact of the drop-out constraint on equilibrium trading rates.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"34 4","pages":"1123-1166"},"PeriodicalIF":1.6,"publicationDate":"2024-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139481058","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":"Study on the validity of the theoretical paradigm of art therapy for vulnerable children.","authors":"Hongyi Fang, Yanhua Li, Misi Wu, Feng Gan","doi":"10.1080/17483107.2022.2074555","DOIUrl":"10.1080/17483107.2022.2074555","url":null,"abstract":"<p><strong>Purpose: </strong>The vulnerable children refer to the special group of children with deviation in the process of children's psychological development and personality formation due to growth dilemmas.</p><p><strong>Materials and methods: </strong>This may incur a series of serious social and family problems. The vulnerable children mainly cover the children suffering from children's psychological problems, such as childhood autism, autism, social anxiety and hypersensitivity, fear, depression, and PTSD arising from other factors. At present, the research results at home and abroad mainly focus on the psychological dynamic correlation investigation and solution discussion of a certain kind of difficult factor in the children's psychological development based on statistical data by the experimental methods, such as scale and model, and there is a blind spot in the humanistic orientation theory construction of psychological treatment for vulnerable children, causing the social reflection on children's psychological predicament from the humanistic perspective cannot be performed in related researches and going against searching for universal and integral theoretical paradigm for solving related problems.</p><p><strong>Results: </strong>Sophisticated technologies for the observations have emerged increasingly for enabling the psychological features of vulnerable children through developmental cognitive neuroscience experiments.</p><p><strong>Conclusion: </strong>This paper introduces humanistic art therapy theory, focuses on the construction of a theoretical paradigm, and verifies its effectiveness based on the experimental results on the psychological development of vulnerable children, with an efficient performance.IMPLICATIONS FOR REHABILITATIONThis study mainly refers to children with difficulty in social inclusion and psychological development.The results showed that two kinds of art therapy can obviously improve the psychological disorders of vulnerable children.The goal was to enhance self-cognition, strengthen emotional interaction, and implement positive motivation.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"11 1","pages":"188-199"},"PeriodicalIF":2.2,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84689944","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":"Almost strong equilibria for time-inconsistent stopping problems under finite horizon in continuous time","authors":"Zhou Zhou","doi":"10.1111/mafi.12428","DOIUrl":"10.1111/mafi.12428","url":null,"abstract":"<p>We consider time-inconsistent stopping problems for a continuous-time Markov chain under finite time horizon with non-exponential discounting. We provide an example indicating that strong equilibria may not exist in general. As a result, we propose a notion of equilibrium called almost strong equilibrium (ASE), which is a weak equilibrium and satisfies the condition of strong equilibria except at the boundary points of the associated stopping region. We provide an iteration procedure and show that this procedure leads to an ASE. Moreover, we prove that this ASE is the unique ASE among all regular stopping policies under finite horizon <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 <mo>&lt;</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$T&amp;lt;infty$</annotation>\u0000 </semantics></math>. In contrast, we show that strong equilibria (and thus ASE) exist and may not be unique for the infinite horizon case <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 <mo>=</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$T=infty$</annotation>\u0000 </semantics></math>. Furthermore, we show that the limit of the finite-horizon ASE as <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 <mo>→</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$Trightarrow infty$</annotation>\u0000 </semantics></math> is a weak equilibrium for the infinite-horizon problem, and may not be a strong equilibrium or ASE.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"34 4","pages":"1089-1122"},"PeriodicalIF":1.6,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mafi.12428","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139035134","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":"GANs training: A game and stochastic control approach","authors":"Xin Guo,&nbsp;Othmane Mounjid","doi":"10.1111/mafi.12427","DOIUrl":"10.1111/mafi.12427","url":null,"abstract":"<p>Training generative adversarial networks (GANs) are known to be difficult, especially for financial time series. This paper first analyzes the well-posedness problem in GANs minimax games and the widely recognized convexity issue in GANs objective functions. It then proposes a stochastic control framework for hyper-parameters tuning in GANs training. The weak form of dynamic programming principle and the uniqueness and the existence of the value function in the viscosity sense for the corresponding minimax game are established. In particular, explicit forms for the optimal adaptive learning rate and batch size are derived and are shown to depend on the convexity of the objective function, revealing a relation between improper choices of learning rate and explosion in GANs training. Finally, empirical studies demonstrate that training algorithms incorporating this adaptive control approach outperform the standard ADAM method in terms of convergence and robustness. From GANs training perspective, the analysis in this paper provides analytical support for the popular practice of “clipping,” and suggests that the convexity and well-posedness issues in GANs may be tackled through appropriate choices of hyper-parameters.</p>","PeriodicalId":49867,"journal":{"name":"Mathematical Finance","volume":"34 2","pages":"522-556"},"PeriodicalIF":1.6,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138823991","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}