Abstract The statistical functional expectile has recently attracted the attention of researchers in the area of risk management, because it is the only risk measure that is both coherent and elicitable. In this article, we consider the portfolio optimization problem with an expectile objective. Portfolio optimization problems corresponding to other risk measures are often solved by formulating a linear program (LP) that is based on a sample of asset returns. We derive three different LP formulations for the portfolio expectile optimization problem, which can be considered as counterparts to the LP formulations for the Conditional Value-at-Risk (CVaR) objective in the works of Rockafellar and Uryasev [43], Ogryczak and Śliwiński [41] and Espinoza and Moreno [21]. When the LPs are based on a simulated sample of the true (assumed continuous) asset returns distribution, the portfolios obtained from the LPs are only approximately optimal. We conduct a numerical case study estimating the suboptimality of the approximate portfolios depending on the sample size, number of assets, and tail-heaviness of the asset returns distribution. Further, the computation times using the three LP formulations are analyzed, showing that the formulation that is based on a scenario aggregation approach is considerably faster than the two alternatives.
{"title":"Scenario aggregation method for portfolio expectile optimization","authors":"E. Jakobsons","doi":"10.1515/strm-2016-0008","DOIUrl":"https://doi.org/10.1515/strm-2016-0008","url":null,"abstract":"Abstract The statistical functional expectile has recently attracted the attention of researchers in the area of risk management, because it is the only risk measure that is both coherent and elicitable. In this article, we consider the portfolio optimization problem with an expectile objective. Portfolio optimization problems corresponding to other risk measures are often solved by formulating a linear program (LP) that is based on a sample of asset returns. We derive three different LP formulations for the portfolio expectile optimization problem, which can be considered as counterparts to the LP formulations for the Conditional Value-at-Risk (CVaR) objective in the works of Rockafellar and Uryasev [43], Ogryczak and Śliwiński [41] and Espinoza and Moreno [21]. When the LPs are based on a simulated sample of the true (assumed continuous) asset returns distribution, the portfolios obtained from the LPs are only approximately optimal. We conduct a numerical case study estimating the suboptimality of the approximate portfolios depending on the sample size, number of assets, and tail-heaviness of the asset returns distribution. Further, the computation times using the three LP formulations are analyzed, showing that the formulation that is based on a scenario aggregation approach is considerably faster than the two alternatives.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2016-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/strm-2016-0008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67314762","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}
In this paper we study the valuation problem of an insurance company by maximizing the expected discounted future dividend payments in a model with partial information that allows for a changing economic environment. The surplus process is modeled as a Brownian motion with drift. This drift depends on an underlying Markov chain the current state of which is assumed to be unobservable. The different states of the Markov chain thereby represent different phases of the economy. We apply results from filtering theory to overcome uncertainty and then we give an analytic characterization of the optimal value function. Finally, we present a numerical study covering various scenarios to get a clear picture of how dividends should be paid out.
{"title":"Dividend maximization in a hidden Markov switching model","authors":"Michaela Szolgyenyi","doi":"10.1515/strm-2015-0019","DOIUrl":"https://doi.org/10.1515/strm-2015-0019","url":null,"abstract":"In this paper we study the valuation problem of an insurance company by maximizing the expected discounted future dividend payments in a model with partial information that allows for a changing economic environment. The surplus process is modeled as a Brownian motion with drift. This drift depends on an underlying Markov chain the current state of which is assumed to be unobservable. The different states of the Markov chain thereby represent different phases of the economy. We apply results from filtering theory to overcome uncertainty and then we give an analytic characterization of the optimal value function. Finally, we present a numerical study covering various scenarios to get a clear picture of how dividends should be paid out.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2016-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/strm-2015-0019","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67313604","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}
Abstract We consider an investor facing a classical portfolio problem of optimal investment in a log-Brownian stock and a fixed-interest bond, but constrained to choose portfolio and consumption strategies that reduce a dynamic shortfall risk measure. For continuous- and discrete-time financial markets we investigate the loss in expected utility of intermediate consumption and terminal wealth caused by imposing a dynamic risk constraint. We derive the dynamic programming equations for the resulting stochastic optimal control problems and solve them numerically. Our numerical results indicate that the loss of portfolio performance is not too large while the risk is notably reduced. We then investigate time discretization effects and find that the loss of portfolio performance resulting from imposing a risk constraint is typically bigger than the loss resulting from infrequent trading.
{"title":"Portfolio optimization under dynamic risk constraints: Continuous vs. discrete time trading","authors":"I. Redeker, R. Wunderlich","doi":"10.1515/strm-2017-0001","DOIUrl":"https://doi.org/10.1515/strm-2017-0001","url":null,"abstract":"Abstract We consider an investor facing a classical portfolio problem of optimal investment in a log-Brownian stock and a fixed-interest bond, but constrained to choose portfolio and consumption strategies that reduce a dynamic shortfall risk measure. For continuous- and discrete-time financial markets we investigate the loss in expected utility of intermediate consumption and terminal wealth caused by imposing a dynamic risk constraint. We derive the dynamic programming equations for the resulting stochastic optimal control problems and solve them numerically. Our numerical results indicate that the loss of portfolio performance is not too large while the risk is notably reduced. We then investigate time discretization effects and find that the loss of portfolio performance resulting from imposing a risk constraint is typically bigger than the loss resulting from infrequent trading.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2016-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/strm-2017-0001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67314936","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}
Abstract This paper is concerned with a procedure for financial time series clustering, aimed at creating groups of time series characterized by similar behavior with regard to extreme events. The core of our proposal is a double clustering procedure: the former is based on the lower tail dependence of all the possible pairs of time series, the latter on the upper tail dependence. Tail dependence coefficients are estimated with copula functions. The final goal is to exploit the two clustering solutions in an algorithm designed to create a portfolio that maximizes the probability of joint positive extreme returns while minimizing the risk of joint negative extreme returns. In financial crisis scenarios, such a portfolio is expected to outperform portfolios generated by the traditional methods. We describe the results of a simulation study and, finally, we apply the procedure to a dataset composed of the 50 assets included in the EUROSTOXX index.
{"title":"A double clustering algorithm for financial time series based on extreme events","authors":"G. De Luca, P. Zuccolotto","doi":"10.1515/strm-2015-0026","DOIUrl":"https://doi.org/10.1515/strm-2015-0026","url":null,"abstract":"Abstract This paper is concerned with a procedure for financial time series clustering, aimed at creating groups of time series characterized by similar behavior with regard to extreme events. The core of our proposal is a double clustering procedure: the former is based on the lower tail dependence of all the possible pairs of time series, the latter on the upper tail dependence. Tail dependence coefficients are estimated with copula functions. The final goal is to exploit the two clustering solutions in an algorithm designed to create a portfolio that maximizes the probability of joint positive extreme returns while minimizing the risk of joint negative extreme returns. In financial crisis scenarios, such a portfolio is expected to outperform portfolios generated by the traditional methods. We describe the results of a simulation study and, finally, we apply the procedure to a dataset composed of the 50 assets included in the EUROSTOXX index.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/strm-2015-0026","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67314297","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}
Abstract This paper provides a framework for modeling the financial system with multiple illiquid assets when liquidation of illiquid assets is caused by failure to meet a leverage requirement. This extends the network model of [6] which incorporates a single asset with fire sales and capital adequacy ratio. This also extends the network model of [14] which incorporates multiple illiquid assets with fire sales and no leverage ratios. We prove existence of equilibrium clearing payments and liquidation prices for a known liquidation strategy when leverage requirements are required. We also prove sufficient conditions for the existence of an equilibrium liquidation strategy with corresponding clearing payments and liquidation prices. Finally, we calibrate network models to asset and liability data for 50 banks in the United States from 2007–2014 in order to draw conclusions on systemic risk as a function of leverage requirements.
{"title":"The effects of leverage requirements and fire sales on financial contagion via asset liquidation strategies in financial networks","authors":"Zachary Feinstein, Fatena El-Masri","doi":"10.1515/strm-2015-0030","DOIUrl":"https://doi.org/10.1515/strm-2015-0030","url":null,"abstract":"Abstract This paper provides a framework for modeling the financial system with multiple illiquid assets when liquidation of illiquid assets is caused by failure to meet a leverage requirement. This extends the network model of [6] which incorporates a single asset with fire sales and capital adequacy ratio. This also extends the network model of [14] which incorporates multiple illiquid assets with fire sales and no leverage ratios. We prove existence of equilibrium clearing payments and liquidation prices for a known liquidation strategy when leverage requirements are required. We also prove sufficient conditions for the existence of an equilibrium liquidation strategy with corresponding clearing payments and liquidation prices. Finally, we calibrate network models to asset and liability data for 50 banks in the United States from 2007–2014 in order to draw conclusions on systemic risk as a function of leverage requirements.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2015-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/strm-2015-0030","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67314041","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}
Abstract This paper analyzes the topology of the network of common asset holdings, where nodes represent managed portfolios and edge weights capture the impact of liquidations. Asset holdings data is extracted from the 13F filings. We consider the degree centrality as the degree in the subnetwork of weak links, where weak links are those that lead to significant liquidations. We explore the applications of this network representation to clustering and forecasting. To validate the weight attribution and the threshold used to define the weak links, we show that the degree centrality is correlated with excess returns, and is significant after we control for the Carhart four factors. The network of weak links has a scale free structure, similar to financial networks of balance sheet exposures. Moreover, a small number of clusters, densely linked, concentrate a significant proportion of the portfolios.
{"title":"The topology of overlapping portfolio networks","authors":"Weilong Guo, Andreea Minca, Li Wang","doi":"10.1515/strm-2015-0020","DOIUrl":"https://doi.org/10.1515/strm-2015-0020","url":null,"abstract":"Abstract This paper analyzes the topology of the network of common asset holdings, where nodes represent managed portfolios and edge weights capture the impact of liquidations. Asset holdings data is extracted from the 13F filings. We consider the degree centrality as the degree in the subnetwork of weak links, where weak links are those that lead to significant liquidations. We explore the applications of this network representation to clustering and forecasting. To validate the weight attribution and the threshold used to define the weak links, we show that the degree centrality is correlated with excess returns, and is significant after we control for the Carhart four factors. The network of weak links has a scale free structure, similar to financial networks of balance sheet exposures. Moreover, a small number of clusters, densely linked, concentrate a significant proportion of the portfolios.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2015-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/strm-2015-0020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67313724","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}
M. Hofert, Amir Memartoluie, D. Saunders, T. Wirjanto
Abstract Numerical challenges inherent in algorithms for computing worst Value-at-Risk in homogeneous portfolios are identified and solutions as well as words of warning concerning their implementation are provided. Furthermore, both conceptual and computational improvements to the Rearrangement Algorithm for approximating worst Value-at-Risk for portfolios with arbitrary marginal loss distributions are given. In particular, a novel Adaptive Rearrangement Algorithm is introduced and investigated. These algorithms are implemented using the R package qrmtools and may be of interest in any context in which it is required to find columnwise permutations of a matrix such that the minimal (maximal) row sum is maximized (minimized).
{"title":"Improved algorithms for computing worst Value-at-Risk","authors":"M. Hofert, Amir Memartoluie, D. Saunders, T. Wirjanto","doi":"10.1515/strm-2015-0028","DOIUrl":"https://doi.org/10.1515/strm-2015-0028","url":null,"abstract":"Abstract Numerical challenges inherent in algorithms for computing worst Value-at-Risk in homogeneous portfolios are identified and solutions as well as words of warning concerning their implementation are provided. Furthermore, both conceptual and computational improvements to the Rearrangement Algorithm for approximating worst Value-at-Risk for portfolios with arbitrary marginal loss distributions are given. In particular, a novel Adaptive Rearrangement Algorithm is introduced and investigated. These algorithms are implemented using the R package qrmtools and may be of interest in any context in which it is required to find columnwise permutations of a matrix such that the minimal (maximal) row sum is maximized (minimized).","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2015-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/strm-2015-0028","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67313940","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}
Abstract In this paper we study time-consistent risk measures for returns that are given by a GARCH(1,1) model. We present a construction of risk measures based on their static counterparts that overcomes the lack of time-consistency. We then study in detail our construction for the risk measures Value-at-Risk (VaR) and Average Value-at-Risk (AVaR). While in the VaR case we can derive an analytical formula for its time-consistent counterpart, in the AVaR case we derive lower and upper bounds to its time-consistent version. Furthermore, we incorporate techniques from extreme value theory (EVT) to allow for a more tail-geared statistical analysis of the corresponding risk measures. We conclude with an application of our results to a data set of stock prices.
{"title":"Time-consistency of risk measures with GARCH volatilities and their estimation","authors":"C. Klüppelberg, Jianing Zhang","doi":"10.1515/strm-2015-0010","DOIUrl":"https://doi.org/10.1515/strm-2015-0010","url":null,"abstract":"Abstract In this paper we study time-consistent risk measures for returns that are given by a GARCH(1,1) model. We present a construction of risk measures based on their static counterparts that overcomes the lack of time-consistency. We then study in detail our construction for the risk measures Value-at-Risk (VaR) and Average Value-at-Risk (AVaR). While in the VaR case we can derive an analytical formula for its time-consistent counterpart, in the AVaR case we derive lower and upper bounds to its time-consistent version. Furthermore, we incorporate techniques from extreme value theory (EVT) to allow for a more tail-geared statistical analysis of the corresponding risk measures. We conclude with an application of our results to a data set of stock prices.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2015-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/strm-2015-0010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67313763","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}
Abstract We consider two nonparametric estimators for the risk measure of the sum of n i.i.d. individual insurance risks where the number of historical single claims that are used for the statistical estimation is of order n. This framework matches the situation that nonlife insurance companies are faced with within the scope of premium calculation. Indeed, the risk measure of the aggregate risk divided by n can be seen as a suitable premium for each of the individual risks. For both estimators divided by n we derive a sort of Marcinkiewicz–Zygmund strong law as well as a weak limit theorem. The behavior of the estimators for small to moderate n is studied by means of Monte-Carlo simulations.
{"title":"Nonparametric estimation of risk measures of collective risks","authors":"A. Lauer, Henryk Zähle","doi":"10.1515/strm-2015-0014","DOIUrl":"https://doi.org/10.1515/strm-2015-0014","url":null,"abstract":"Abstract We consider two nonparametric estimators for the risk measure of the sum of n i.i.d. individual insurance risks where the number of historical single claims that are used for the statistical estimation is of order n. This framework matches the situation that nonlife insurance companies are faced with within the scope of premium calculation. Indeed, the risk measure of the aggregate risk divided by n can be seen as a suitable premium for each of the individual risks. For both estimators divided by n we derive a sort of Marcinkiewicz–Zygmund strong law as well as a weak limit theorem. The behavior of the estimators for small to moderate n is studied by means of Monte-Carlo simulations.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2015-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/strm-2015-0014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67313914","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}
After a quick review of superpositions of OU (supOU) processes, integrated supOU processes and the supOU stochastic volatility model we estimate these processes by using the generalized method of moments (GMM). We show that the GMM approach yields consistent estimators and that it works very well in practice. Moreover, we discuss the influence of long memory effects.
{"title":"Moment based estimation of supOU processes and a related stochastic volatility model","authors":"Stelzer Robert, Wittlinger Marc, Tosstorff Thomas","doi":"10.1515/STRM-2012-1152","DOIUrl":"https://doi.org/10.1515/STRM-2012-1152","url":null,"abstract":"After a quick review of superpositions of OU (supOU) processes, integrated supOU processes and the supOU stochastic volatility model we estimate these processes by using the generalized method of moments (GMM). We show that the GMM approach yields consistent estimators and that it works very well in practice. Moreover, we discuss the influence of long memory effects.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2015-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/STRM-2012-1152","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67312828","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：