Abstract We consider a portfolio optimization problem of the Black–Litterman type, in which we use the conditional value-at-risk (CVaR) as the risk measure and we use the multi-variate elliptical distributions, instead of the multi-variate normal distribution, to model the financial asset returns. We propose an approximation algorithm and establish the convergence results. Based on the approximation algorithm, we derive a closed-form solution of the portfolio optimization problems of the Black–Litterman type with CVaR.
{"title":"A Closed-Form Solution of the Black-Litterman Model with Conditional Value at Risk","authors":"Tao Pang, Cagatay Karan","doi":"10.2139/ssrn.2862165","DOIUrl":"https://doi.org/10.2139/ssrn.2862165","url":null,"abstract":"Abstract We consider a portfolio optimization problem of the Black–Litterman type, in which we use the conditional value-at-risk (CVaR) as the risk measure and we use the multi-variate elliptical distributions, instead of the multi-variate normal distribution, to model the financial asset returns. We propose an approximation algorithm and establish the convergence results. Based on the approximation algorithm, we derive a closed-form solution of the portfolio optimization problems of the Black–Litterman type with CVaR.","PeriodicalId":246078,"journal":{"name":"OPER: Computational Techniques (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131096961","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}
We analyze the fluctuation of the loss from default around its large portfolio limit in a class of reduced-form models of correlated firm-by-firm default timing. We prove a weak convergence result for the fluctuation process and use it for developing a conditionally Gaussian approximation to the loss distribution. Numerical results illustrate the accuracy and computational efficiency of the approximation.
{"title":"Fluctuation Analysis for the Loss from Default","authors":"K. Spiliopoulos, Justin A. Sirignano, K. Giesecke","doi":"10.2139/ssrn.2226994","DOIUrl":"https://doi.org/10.2139/ssrn.2226994","url":null,"abstract":"We analyze the fluctuation of the loss from default around its large portfolio limit in a class of reduced-form models of correlated firm-by-firm default timing. We prove a weak convergence result for the fluctuation process and use it for developing a conditionally Gaussian approximation to the loss distribution. Numerical results illustrate the accuracy and computational efficiency of the approximation.","PeriodicalId":246078,"journal":{"name":"OPER: Computational Techniques (Topic)","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131103181","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}
We provide a sequential Monte Carlo method for estimating rare-event probabilities in dynamic, intensity-based point process models of portfolio credit risk. The method is based on a change of measure and involves a resampling mechanism. We propose resampling weights that lead, under technical conditions, to a logarithmically efficient simulation estimator of the probability of large portfolio losses. A numerical analysis illustrates the features of the method and contrasts it with other rare-event schemes recently developed for portfolio credit risk, including an interacting particle scheme and an importance sampling scheme.
{"title":"Sequential Importance Sampling and Resampling for Dynamic Portfolio Credit Risk","authors":"Shaojie Deng, K. Giesecke, T. Lai","doi":"10.2139/ssrn.1674204","DOIUrl":"https://doi.org/10.2139/ssrn.1674204","url":null,"abstract":"We provide a sequential Monte Carlo method for estimating rare-event probabilities in dynamic, intensity-based point process models of portfolio credit risk. The method is based on a change of measure and involves a resampling mechanism. We propose resampling weights that lead, under technical conditions, to a logarithmically efficient simulation estimator of the probability of large portfolio losses. A numerical analysis illustrates the features of the method and contrasts it with other rare-event schemes recently developed for portfolio credit risk, including an interacting particle scheme and an importance sampling scheme.","PeriodicalId":246078,"journal":{"name":"OPER: Computational Techniques (Topic)","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121822205","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}
Random graph generation is an important tool for studying large complex networks. Despite abundance of random graph models, constructing models with application-driven constraints is poorly understood. In order to advance state-of-the-art in this area, we focus on random graphs without short cycles as a stylized family of graphs, and propose the RandGraph algorithm for randomly generating them. For any constant k, when m=O(n^{1+1/[2k(k+3)]}), RandGraph generates an asymptotically uniform random graph with n vertices, m edges, and no cycle of length at most k using O(n^2m) operations. We also characterize the approximation error for finite values of n. To the best of our knowledge, this is the first polynomial-time algorithm for the problem. RandGraph works by sequentially adding $m$ edges to an empty graph with n vertices. Recently, such sequential algorithms have been successful for random sampling problems. Our main contributions to this line of research includes introducing a new approach for sequentially approximating edge-specific probabilities at each step of the algorithm, and providing a new method for analyzing such algorithms.
{"title":"Generating Random Networks Without Short Cycles","authors":"M. Bayati, A. Montanari, A. Saberi","doi":"10.2139/ssrn.2848110","DOIUrl":"https://doi.org/10.2139/ssrn.2848110","url":null,"abstract":"Random graph generation is an important tool for studying large complex networks. Despite abundance of random graph models, constructing models with application-driven constraints is poorly understood. In order to advance state-of-the-art in this area, we focus on random graphs without short cycles as a stylized family of graphs, and propose the RandGraph algorithm for randomly generating them. For any constant k, when m=O(n^{1+1/[2k(k+3)]}), RandGraph generates an asymptotically uniform random graph with n vertices, m edges, and no cycle of length at most k using O(n^2m) operations. We also characterize the approximation error for finite values of n. To the best of our knowledge, this is the first polynomial-time algorithm for the problem. RandGraph works by sequentially adding $m$ edges to an empty graph with n vertices. Recently, such sequential algorithms have been successful for random sampling problems. Our main contributions to this line of research includes introducing a new approach for sequentially approximating edge-specific probabilities at each step of the algorithm, and providing a new method for analyzing such algorithms.","PeriodicalId":246078,"journal":{"name":"OPER: Computational Techniques (Topic)","volume":"120 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2008-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125930772","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}
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