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Mean field games with unbounded controlled common noise in portfolio management with relative performance criteria 具有相对绩效标准的投资组合管理中无约束受控普通噪声的均值场博弈
IF 1.6 3区 经济学
Mathematics and Financial Economics Pub Date : 2024-09-19 DOI: 10.1007/s11579-024-00363-1
Panagiotis E. Souganidis, Thaleia Zariphopoulou
{"title":"Mean field games with unbounded controlled common noise in portfolio management with relative performance criteria","authors":"Panagiotis E. Souganidis, Thaleia Zariphopoulou","doi":"10.1007/s11579-024-00363-1","DOIUrl":"https://doi.org/10.1007/s11579-024-00363-1","url":null,"abstract":"<p>Motivated by optimal allocation models with relative performance criteria, we introduce a mean field game in which the terminal expected utility of the representative agent depends on her own state as well as the average of her peers. We derive the master equation, which, in view of the presence of controls in the volatility, needs to be coupled with a compatibility condition for the mean field optimal feedback control. We concentrate on the class of separable payoffs under both general utilities and couplings. We derive a solution to the master equation and find the associated optimal feedback control expressed via the value function in the absence of competition and a dynamic coupling function solving a non-local quasilinear equation. In turn, we construct the related optimal state and control processes, and give representative examples. Projecting the mean field solutions on finite dimensions, we recover the solution of the <i>N</i>-game for linear couplings and arbitrary utilities, and we study the proximity of these approximations to their <i>N</i>-player game counterparts.</p>","PeriodicalId":48722,"journal":{"name":"Mathematics and Financial Economics","volume":"162 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248620","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
Optimal investment and reinsurance strategies for an insurer with regime-switching 制度切换型保险公司的最佳投资和再保险策略
IF 1.6 3区 经济学
Mathematics and Financial Economics Pub Date : 2024-08-21 DOI: 10.1007/s11579-024-00374-y
Weiwei Shen
{"title":"Optimal investment and reinsurance strategies for an insurer with regime-switching","authors":"Weiwei Shen","doi":"10.1007/s11579-024-00374-y","DOIUrl":"https://doi.org/10.1007/s11579-024-00374-y","url":null,"abstract":"<p>This paper considers the issue of optimal investment and reinsurance strategies for an insurer with regime-switching. In our mathematical model, a risk-free asset and a risky asset are assumed to rely on a continuous time-homogeneous, finite-state, observed Markov chain, and the latter’s price dynamics is described by a general regime-switching jump-diffusion process. We are extending the classical claim process to a Markov-modulated compound Poisson process. The insurer faces the decision-making problem of choosing to invest his/her surplus in the financial market and purchase reinsurance such that the expected power utility of his/her terminal wealth is maximized. We apply dynamic programming principle to derive the regime-switching Hamilton–Jacobi–Bellman (HJB) equation. Then, by analysing the solutions of the HJB equation, the optimal investment and reinsurance strategies are obtained and given in the verification theorem. Finally, the numerical analysis based on a two-state Markov chain is presented to illustrate our results.</p>","PeriodicalId":48722,"journal":{"name":"Mathematics and Financial Economics","volume":"11 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142181931","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
Irreversible reinsurance: minimization of capital injections in presence of a fixed cost 不可逆再保险：在存在固定成本的情况下尽量减少注资
IF 1.6 3区 经济学
Mathematics and Financial Economics Pub Date : 2024-08-04 DOI: 10.1007/s11579-024-00373-z
Salvatore Federico, Giorgio Ferrari, Maria-Laura Torrente
{"title":"Irreversible reinsurance: minimization of capital injections in presence of a fixed cost","authors":"Salvatore Federico, Giorgio Ferrari, Maria-Laura Torrente","doi":"10.1007/s11579-024-00373-z","DOIUrl":"https://doi.org/10.1007/s11579-024-00373-z","url":null,"abstract":"<p>We propose a model in which, in exchange to the payment of a fixed transaction cost, an insurance company can choose the retention level as well as the time at which subscribing a perpetual reinsurance contract. The surplus process of the insurance company evolves according to the diffusive approximation of the Cramér-Lundberg model, claims arrive at a fixed constant rate, and the distribution of their sizes is general. Furthermore, we do not specify any particular functional form of the retention level. The aim of the company is to take actions in order to minimize the sum of the expected value of the total discounted flow of capital injections needed to avoid bankruptcy and of the fixed activation cost of the reinsurance contract. We provide an explicit solution to this problem, which involves the resolution of a static nonlinear optimization problem and of an optimal stopping problem for a reflected diffusion. We then illustrate the theoretical results in the case of proportional and excess-of-loss reinsurance, by providing a numerical study of the dependency of the optimal solution with respect to the model’s parameters.</p>","PeriodicalId":48722,"journal":{"name":"Mathematics and Financial Economics","volume":"30 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141946253","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
Age-dependent robust strategic asset allocation with inflation–deflation hedging demand 具有通胀-通缩对冲需求的与年龄相关的稳健战略资产配置
IF 1.6 3区 经济学
Mathematics and Financial Economics Pub Date : 2024-07-26 DOI: 10.1007/s11579-024-00369-9
Kentaro Kikuchi, Koji Kusuda
{"title":"Age-dependent robust strategic asset allocation with inflation–deflation hedging demand","authors":"Kentaro Kikuchi, Koji Kusuda","doi":"10.1007/s11579-024-00369-9","DOIUrl":"https://doi.org/10.1007/s11579-024-00369-9","url":null,"abstract":"<p>This study analyzes robust strategic asset allocation under a quadratic security market model with stochastic volatility and inflation rates assuming “age-dependent robust utility” in which relative ambiguity aversion is a decreasing function of age. We show that, unlike homothetic robust utility, age-dependent robust utility cannot be interpreted as homothetic stochastic differential utility. We consider the finite-time consumption-investment problem and derive a linear approximate optimal robust portfolio candidate decomposed into myopic, intertemporal hedging, and inflation–deflation hedging demands. Our numerical analysis of the approximate optimal allocation to the S &amp;P500 shows modest hump-shaped age effects, similar to the results of a previous empirical analysis, and that the upswing is due to the increase in myopic demand, while the downswing is due to the decrease in intertemporal hedging demand.</p>","PeriodicalId":48722,"journal":{"name":"Mathematics and Financial Economics","volume":"42 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141781733","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
Robust long-term growth rate of expected utility for leveraged ETFs 杠杆 ETF 预期效用的长期稳健增长率
IF 1.6 3区 经济学
Mathematics and Financial Economics Pub Date : 2024-07-26 DOI: 10.1007/s11579-024-00371-1
Tim Leung, Hyungbin Park, Heejun Yeo
{"title":"Robust long-term growth rate of expected utility for leveraged ETFs","authors":"Tim Leung, Hyungbin Park, Heejun Yeo","doi":"10.1007/s11579-024-00371-1","DOIUrl":"https://doi.org/10.1007/s11579-024-00371-1","url":null,"abstract":"<p>This paper analyzes the robust long-term growth rate of expected utility and expected return from holding a leveraged exchange-traded fund. When the Markovian model parameters in the reference asset are uncertain, the robust long-term growth rate is derived by analyzing the worst-case parameters among an uncertainty set. We compute the growth rate and describe the optimal leverage ratio maximizing the robust long-term growth rate. To achieve this, the worst-case parameters are analyzed by the comparison principle, and the growth rate of the worst-case is computed using the Hansen–Scheinkman decomposition. The robust long-term growth rates are obtained explicitly under a number of models for the reference asset, including the geometric Brownian motion, Cox–Ingersoll–Ross, 3/2, and Heston and 3/2 stochastic volatility models. Additionally, we demonstrate the impact of stochastic interest rates, such as the Vasicek and inverse GARCH short rate models. This paper is an extended work of Leung and Park (Int J Theor Appl Finance 20(6):1750037, 2017).</p>","PeriodicalId":48722,"journal":{"name":"Mathematics and Financial Economics","volume":"63 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141781734","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
Caballero–Engel meet Lasry–Lions: A uniqueness result Caballero-Engel 遇见 Lasry-Lions：唯一性结果
IF 1.6 3区 经济学
Mathematics and Financial Economics Pub Date : 2024-07-26 DOI: 10.1007/s11579-024-00370-2
Fernando Alvarez, Francesco Lippi, Panagiotis Souganidis
{"title":"Caballero–Engel meet Lasry–Lions: A uniqueness result","authors":"Fernando Alvarez, Francesco Lippi, Panagiotis Souganidis","doi":"10.1007/s11579-024-00370-2","DOIUrl":"https://doi.org/10.1007/s11579-024-00370-2","url":null,"abstract":"<p>In a Mean Field Game (MFG) each decision maker cares about the cross sectional distribution of the state and the dynamics of the distribution is generated by the agents’ optimal decisions. We prove the uniqueness of the equilibrium in a class of MFG where the decision maker controls the state at optimally chosen times. This setup accommodates several problems featuring non-convex adjustment costs, and complements the well known drift-control case studied by Lasry–Lions. Examples of such problems are described by Caballero and Engel in several papers, which introduce the concept of the generalized hazard function of adjustment. We extend the analysis to a general “impulse control problem” by introducing the concept of the “Impulse Hamiltonian”. Under the monotonicity assumption (a form of strategic substitutability), we establish the uniqueness of equilibrium. In this context, the Impulse Hamiltonian and its derivative play a similar role to the classical Hamiltonian that arises in the drift-control case.\u0000</p>","PeriodicalId":48722,"journal":{"name":"Mathematics and Financial Economics","volume":"9 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141781735","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
On the value of a time-inconsistent mean-field zero-sum Dynkin game 论时间不一致均场零和戴恩金博弈的价值
IF 1.6 3区 经济学
Mathematics and Financial Economics Pub Date : 2024-07-03 DOI: 10.1007/s11579-024-00367-x
Boualem Djehiche
{"title":"On the value of a time-inconsistent mean-field zero-sum Dynkin game","authors":"Boualem Djehiche","doi":"10.1007/s11579-024-00367-x","DOIUrl":"https://doi.org/10.1007/s11579-024-00367-x","url":null,"abstract":"<p>We study a mean-field zero-sum Dynkin game (MF-ZSDG) with time-inconsistent performance functionals adapted to the Brownian filtration. Despite the time-inconsistency of the MF-ZSDG, we show that it admits a value and that the pair of first times the value process hits the upper and lower obstacles, respectively, is a saddle point for the game. We solve the problem by approximating the associated lower and upper value processes with a sequence of value processes of interacting time-consistent zero-sum Dynkin games for which the saddle point of each of the value processes is the pair of first times each of those value processes hits the associated upper and lower obstacles, respectively. Under mild assumptions, we show that this sequence of saddle points converges in probability to the pair of first hitting times of the value process of the upper and lower obstacles, respectively, and that the limit is a saddle point for the time-inconsistent MF-ZSDG.</p>","PeriodicalId":48722,"journal":{"name":"Mathematics and Financial Economics","volume":"38 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548752","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
Are minimum variance portfolios in multi-factor models long in low-beta assets? 多因子模型中的最小方差投资组合是否看多低贝塔资产？
IF 1.6 3区 经济学
Mathematics and Financial Economics Pub Date : 2024-06-29 DOI: 10.1007/s11579-024-00366-y
Ansgar Steland
{"title":"Are minimum variance portfolios in multi-factor models long in low-beta assets?","authors":"Ansgar Steland","doi":"10.1007/s11579-024-00366-y","DOIUrl":"https://doi.org/10.1007/s11579-024-00366-y","url":null,"abstract":"<p>Within the one-factor capital asset pricing model (CAPM), the minimum-variance portfolio (MVP) is known to have long positions in those assets of the underlying investment universe whose betas are less than a well-defined long-short threshold beta. We study the structure of MVPs in more general multi-factor asset pricing models and clarify the low-beta puzzle for multi-factor models: For multi-factor models we derive a similar criterion in terms of the betas with explicit closed-form formulas. But the structural relationship is now more involved and the long-short threshold turns out to be asset-specific. The results rely on recursive inverse-free formulas for the precision matrix, which hold for multi-factor models and allow quick computation of that inverse matrix without the need to invert matrices going beyond diagonal ones. We illustrate our findings by analyzing S &amp;P 500 asset returns. Our empirical results of the S &amp;P 500 constituents between 2019 and 2022 confirm the theoretical findings and shows that the minimum variance portfolio is long in low-beta assets when applying estimates of the established asset-specific thresholds.</p>","PeriodicalId":48722,"journal":{"name":"Mathematics and Financial Economics","volume":"54 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503605","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
Is Kyle’s equilibrium model stable? 凯尔的平衡模型稳定吗？
IF 1.6 3区 经济学
Mathematics and Financial Economics Pub Date : 2024-05-24 DOI: 10.1007/s11579-024-00364-0
Umut Çetin, Kasper Larsen
{"title":"Is Kyle’s equilibrium model stable?","authors":"Umut Çetin, Kasper Larsen","doi":"10.1007/s11579-024-00364-0","DOIUrl":"https://doi.org/10.1007/s11579-024-00364-0","url":null,"abstract":"<p>In the dynamic discrete-time trading setting of Kyle (Econometrica 53:1315–1336, 1985), we prove that Kyle’s equilibrium model is stable when there are one or two trading times. For three or more trading times, we prove that Kyle’s equilibrium is not stable. These theoretical results are proven to hold irrespectively of all Kyle’s input parameters.</p>","PeriodicalId":48722,"journal":{"name":"Mathematics and Financial Economics","volume":"108 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153231","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
An optimal advertising model with carryover effect and mean field terms 一个带有结转效应和平均值项的优化广告模型
IF 1.6 3区 经济学
Mathematics and Financial Economics Pub Date : 2024-05-21 DOI: 10.1007/s11579-024-00361-3
Fausto Gozzi, Federica Masiero, Mauro Rosestolato
{"title":"An optimal advertising model with carryover effect and mean field terms","authors":"Fausto Gozzi, Federica Masiero, Mauro Rosestolato","doi":"10.1007/s11579-024-00361-3","DOIUrl":"https://doi.org/10.1007/s11579-024-00361-3","url":null,"abstract":"<p>We consider a class of optimal advertising problems under uncertainty for the introduction of a new product into the market, on the line of the seminal papers of Vidale and Wolfe (Oper Res 5:370–381, 1957) and Nerlove and Arrow (Economica 29:129–142, 1962). The main features of our model are that, on one side, we assume a carryover effect (i.e. the advertisement spending affects the goodwill with some delay); on the other side we introduce, in the state equation and in the objective, some mean field terms that take into account the presence of other agents. We take the point of view of a planner who optimizes the average profit of all agents, hence we fall into the family of the so-called “Mean Field Control” problems. The simultaneous presence of the carryover effect makes the problem infinite dimensional hence belonging to a family of problems which are very difficult in general and whose study started only very recently, see Cosso et al. [Ann Appl Probab 33(4):2863–2918, 2023]. Here we consider, as a first step, a simple version of the problem providing the solutions in a simple case through a suitable auxiliary problem.</p>","PeriodicalId":48722,"journal":{"name":"Mathematics and Financial Economics","volume":"40 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153179","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
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