{"title":"Expert Opinions and Logarithmic Utility Maximization for Multivariate Stock Returns with Gaussian Drift","authors":"Jörn Sass, Dorothee Westphal, R. Wunderlich","doi":"10.1142/S0219024917500224","DOIUrl":"https://doi.org/10.1142/S0219024917500224","url":null,"abstract":"This paper investigates optimal trading strategies in a financial market with multidimensional stock returns where the drift is an unobservable multivariate Ornstein-Uhlenbeck process. Information about the drift is obtained by observing stock returns and expert opinions. The latter provide unbiased estimates on the current state of the drift at discrete points in time. \u0000The optimal trading strategy of investors maximizing expected logarithmic utility of terminal wealth depends on the filter which is the conditional expectation of the drift given the available information. We state filtering equations to describe its dynamics for different information settings. Between expert opinions this is the Kalman filter. The conditional covariance matrices of the filter follow ordinary differential equations of Riccati type. We rely on basic theory about matrix Riccati equations to investigate their properties. Firstly, we consider the asymptotic behaviour of the covariance matrices for an increasing number of expert opinions on a finite time horizon. Secondly, we state conditions for the convergence of the covariance matrices on an infinite time horizon with regularly arriving expert opinions. \u0000Finally, we derive the optimal trading strategy of an investor. The optimal expected logarithmic utility of terminal wealth, the value function, is a functional of the conditional covariance matrices. Hence, our analysis of the covariance matrices allows us to deduce properties of the value function.","PeriodicalId":286833,"journal":{"name":"arXiv: Portfolio Management","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125919155","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}
{"title":"General Smooth Solutions to the HJB PDE: Applications to Finance","authors":"Moawia Alghalith","doi":"10.2139/SSRN.2684229","DOIUrl":"https://doi.org/10.2139/SSRN.2684229","url":null,"abstract":"We overcome a major obstacle in mathematical optimization. In so doing, we provide a smooth solution to the HJB PDE without assuming the differentiability of the value function. We apply our method to financial models.","PeriodicalId":286833,"journal":{"name":"arXiv: Portfolio Management","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130673736","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}
{"title":"A white noise approach to insider trading","authors":"B. Oksendal, E. Røse","doi":"10.1142/9789813220942_0006","DOIUrl":"https://doi.org/10.1142/9789813220942_0006","url":null,"abstract":"We present a new approach to the optimal portfolio problem for an insider with logarithmic utility. Our method is based on white noise theory, stochastic forward integrals, Hida-Malliavin calculus and the Donsker delta function.","PeriodicalId":286833,"journal":{"name":"arXiv: Portfolio Management","volume":"271 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115597299","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}
{"title":"Risk diversification: a study of persistence with a filtered correlation-network approach","authors":"N. Musmeci, T. Aste, T. Matteo","doi":"10.21314/JNTF.2015.005","DOIUrl":"https://doi.org/10.21314/JNTF.2015.005","url":null,"abstract":"The evolution with time of the correlation structure of equity returns is studied by means of a filtered network approach investigating persistences and recurrences and their implications for risk diversification strategies. We build dynamically Planar Maximally Filtered Graphs from the correlation structure over a rolling window and we study the persistence of the associated Directed Bubble Hierarchical Tree (DBHT) clustering structure. We observe that the DBHT clustering structure is quite stable during the early 2000' becoming gradually less persistent before the unfolding of the 2007-2008 crisis. The correlation structure eventually recovers persistence in the aftermath of the crisis settling up a new phase, distinct from the pre-cysts structure, where the market structure is less related to industrial sector activity. Notably, we observe that - presently - the correlation structure is loosing again persistence indicating the building-up of another, different, phase. Such dynamical changes in persistence and their occurrence at the unfolding of financial crises rises concerns about the effectiveness of correlation-based portfolio management tools for risk diversification.","PeriodicalId":286833,"journal":{"name":"arXiv: Portfolio Management","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125815487","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}
{"title":"Optimal dividend problems for a jump-diffusion model with capital injections and proportional transaction costs","authors":"C. Yin, K. Yuen","doi":"10.3934/JIMO.2015.11.1247","DOIUrl":"https://doi.org/10.3934/JIMO.2015.11.1247","url":null,"abstract":"In this paper, we study the optimal control problem for a company whose surplus process evolves as an upward jump diffusion with random return on investment. Three types of practical optimization problems faced by a company that can control its liquid reserves by paying dividends and injecting capital. In the first problem, we consider the classical dividend problem without capital injections. The second problem aims at maximizing the expected discounted dividend payments minus the expected discounted costs of capital injections over strategies with positive surplus at all times. The third problem has the same objective as the second one, but without the constraints on capital injections. Under the assumption of proportional transaction costs, we identify the value function and the optimal strategies for any distribution of gains.","PeriodicalId":286833,"journal":{"name":"arXiv: Portfolio Management","volume":"29 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125694474","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}
{"title":"Optimal Consumption under Habit Formation In Markets with Transaction Costs and Random Endowments","authors":"Xiang Yu","doi":"10.1214/16-AAP1222","DOIUrl":"https://doi.org/10.1214/16-AAP1222","url":null,"abstract":"This paper studies the optimal consumption under the addictive habit formation preference in markets with transaction costs and unbounded random endowments. To model the proportional transaction costs, we adopt the Kabanov's multi-asset framework with a cash account. At the terminal time T, the investor can receive unbounded random endowments for which we propose a new definition of acceptable portfolios based on the strictly consistent price system (SCPS). We prove a type of super-hedging theorem using the acceptable portfolios which enables us to obtain the consumption budget constraint condition under market frictions. Applying the path dependence reduction and the embedding approach, we obtain the existence and uniqueness of the optimal consumption using some auxiliary processes and the duality analysis. As an application of the duality theory, the market isomorphism with special discounting factors is also discussed in the sense that the original optimal consumption with habit formation is equivalent to the standard optimal consumption problem without the habits impact, however, in a modified isomorphic market model.","PeriodicalId":286833,"journal":{"name":"arXiv: Portfolio Management","volume":"137 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116068505","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}
Y. Lempérière, C. Deremble, P. Seager, M. Potters, J. Bouchaud
{"title":"Two centuries of trend following","authors":"Y. Lempérière, C. Deremble, P. Seager, M. Potters, J. Bouchaud","doi":"10.21314/JOIS.2014.043","DOIUrl":"https://doi.org/10.21314/JOIS.2014.043","url":null,"abstract":"We establish the existence of anomalous excess returns based on trend following strategies across four asset classes (commodities, currencies, stock indices, bonds) and over very long time scales. We use for our studies both futures time series, that exist since 1960, and spot time series that allow us to go back to 1800 on commodities and indices. The overall t-stat of the excess returns is $approx 5$ since 1960 and $approx 10$ since 1800, after accounting for the overall upward drift of these markets. The effect is very stable, both across time and asset classes. It makes the existence of trends one of the most statistically significant anomalies in financial markets. When analyzing the trend following signal further, we find a clear saturation effect for large signals, suggesting that fundamentalist traders do not attempt to resist \"weak trends\", but step in when their own signal becomes strong enough. Finally, we study the performance of trend following in the recent period. We find no sign of a statistical degradation of long trends, whereas shorter trends have significantly withered.","PeriodicalId":286833,"journal":{"name":"arXiv: Portfolio Management","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131052700","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}
{"title":"Merton portfolio problem with one indivisible asset","authors":"Jakub Trybula","doi":"10.4467/20843828AM.15.005.3909","DOIUrl":"https://doi.org/10.4467/20843828AM.15.005.3909","url":null,"abstract":"In this paper we consider a modification of the classical Merton portfolio optimization problem. Namely, an investor can trade in financial asset and consume his capital. He is additionally endowed with a one unit of an indivisible asset which he can sell at any time. We give a numerical example of calculating the optimal time to sale the indivisible asset, the optimal consumption rate and the value function.","PeriodicalId":286833,"journal":{"name":"arXiv: Portfolio Management","volume":"149 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131309557","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}
Zaiwen Wen, X. Peng, Xin Liu, Xiaoling Sun, Xiaodi Bai
{"title":"Asset Allocation under the Basel Accord Risk Measures","authors":"Zaiwen Wen, X. Peng, Xin Liu, Xiaoling Sun, Xiaodi Bai","doi":"10.2139/SSRN.2202845","DOIUrl":"https://doi.org/10.2139/SSRN.2202845","url":null,"abstract":"Financial institutions are currently required to meet more stringent capital requirements than they were before the recent financial crisis; in particular, the capital requirement for a large bank's trading book under the Basel 2.5 Accord more than doubles that under the Basel II Accord. The significant increase in capital requirements renders it necessary for banks to take into account the constraint of capital requirement when they make asset allocation decisions. In this paper, we propose a new asset allocation model that incorporates the regulatory capital requirements under both the Basel 2.5 Accord, which is currently in effect, and the Basel III Accord, which was recently proposed and is currently under discussion. We propose an unified algorithm based on the alternating direction augmented Lagrangian method to solve the model; we also establish the first-order optimality of the limit points of the sequence generated by the algorithm under some mild conditions. The algorithm is simple and easy to implement; each step of the algorithm consists of solving convex quadratic programming or one-dimensional subproblems. Numerical experiments on simulated and real market data show that the algorithm compares favorably with other existing methods, especially in cases in which the model is non-convex.","PeriodicalId":286833,"journal":{"name":"arXiv: Portfolio Management","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128441496","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}