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Mean-risk optimization for index tracking 指数跟踪的平均风险优化
IF 1.5
Statistics & Risk Modeling Pub Date : 2006-07-01 DOI: 10.1524/stnd.2006.24.1.189
Yumiharu Nakano
{"title":"Mean-risk optimization for index tracking","authors":"Yumiharu Nakano","doi":"10.1524/stnd.2006.24.1.189","DOIUrl":"https://doi.org/10.1524/stnd.2006.24.1.189","url":null,"abstract":"SUMMARY This paper presents an analysis of the tracking problems of multiple indices with multidimensional performance criterion consisting of mean wealth and the tracking errors. We evaluate the performance of portfolios via the vector inequalities defined by convex cones, which enable us to describe various preference relations for investors. In Brownian market models with deterministic coefficients, we completely determine the set of efficient portfolios as well as the efficient frontier in our context. As a product of our analysis, we exhibit a version of Tobin's mutual fund theorem.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2006-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1524/stnd.2006.24.1.189","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66892553","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}
引用次数: 0
On distortion functionals 关于畸变泛函
IF 1.5
Statistics & Risk Modeling Pub Date : 2006-07-01 DOI: 10.1524/stnd.2006.24.1.45
G. Pflug
{"title":"On distortion functionals","authors":"G. Pflug","doi":"10.1524/stnd.2006.24.1.45","DOIUrl":"https://doi.org/10.1524/stnd.2006.24.1.45","url":null,"abstract":"SUMMARY Distorted measures have been used in pricing of insurance contracts for a long time. This paper reviews properties of related acceptability functionals in risk management, called distortion functionals. These functionals may be characterized by being mixtures of average values-at-risk. We give a dual representation of these functionals and show how they may be used in portfolio optimization. An iterative numerical procedure for the solution of these portfolio problems is given which is based on duality.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2006-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1524/stnd.2006.24.1.45","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66892741","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}
引用次数: 42
Monetary utility over coherent risk ratios 货币效用高于连贯风险比率
IF 1.5
Statistics & Risk Modeling Pub Date : 2006-07-01 DOI: 10.1524/STND.2006.24.1.173
Johannes Leitner
{"title":"Monetary utility over coherent risk ratios","authors":"Johannes Leitner","doi":"10.1524/STND.2006.24.1.173","DOIUrl":"https://doi.org/10.1524/STND.2006.24.1.173","url":null,"abstract":"SUMMARY For a monetary utility functional U and a coherent risk measure ρ, both with compact scenario sets in Lq, we optimize the ratio α(V): = U(V)/ρ(V) over an (arbitrage-free) linear sub-space V⊆Lp, 1 ≤ p ≤ ∞, of attainable returns in an incomplete market model such that ρ > 0 on V {0}. If a solution Vˆ ∈ V with α(Vˆ) = α¯ V: = sup V∈Vα(V)∈[0,∞) exists, then the first order optimality condition allows to construct an absolutely continuous martingale measure for V as a convex combination Q¯+α¯VQ/1+α¯V of two probability measures Q¯, Q from the respective scenario sets defining U and ρ. Conversely, if α¯V ∈ [0,∞), then α¯V equals the smallest a∈[0,∞) such that Q¯+aQ/1+a is an absolutely continuous martingale measure for V for some probability measures Q¯, Q from the scenario sets defining U, ρ, and α¯V = ∞ holds iff such a convex combination does not exist.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2006-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1524/STND.2006.24.1.173","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66892520","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}
引用次数: 1
Convex risk measures and the dynamics of their penalty functions 凸风险测度及其惩罚函数的动态
IF 1.5
Statistics & Risk Modeling Pub Date : 2006-07-01 DOI: 10.1524/STND.2006.24.1.61
H. Föllmer, Irina Penner
{"title":"Convex risk measures and the dynamics of their penalty functions","authors":"H. Föllmer, Irina Penner","doi":"10.1524/STND.2006.24.1.61","DOIUrl":"https://doi.org/10.1524/STND.2006.24.1.61","url":null,"abstract":"SUMMARY We study various properties of a dynamic convex risk measure for bounded random variables which describe the discounted terminal values of financial positions. In particular we characterize time-consistency by a joint supermartingale property of the risk measure and its penalty function. Moreover we discuss the limit behavior of the risk measure in terms of asymptotic safety and of asymptotic precision, a property which may be viewed as a non-linear analogue of martingale convergence. These results are illustrated by the entropic dynamic risk measure.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2006-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1524/STND.2006.24.1.61","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66892822","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}
引用次数: 214
On the optimal risk allocation problem 关于最优风险分配问题
IF 1.5
Statistics & Risk Modeling Pub Date : 2006-07-01 DOI: 10.1524/stnd.2006.24.1.153
Christian Burgert, L. Rüschendorf
{"title":"On the optimal risk allocation problem","authors":"Christian Burgert, L. Rüschendorf","doi":"10.1524/stnd.2006.24.1.153","DOIUrl":"https://doi.org/10.1524/stnd.2006.24.1.153","url":null,"abstract":"SUMMARY The optimal risk allocation problem or equivalently the problem of risk sharing is the problem to allocate a risk in an optimal way to n traders endowed with risk measures ϱ1, …, ϱn. This problem has a long history in mathematical economics and insurance. In the first part of the paper we review some mathematical tools and discuss their applications to various problems on risk measures related to the allocation problem like to monotonicity properties of optimal allocations, to optimal investment problems or to an appropriate definition of the conditional value at risk. We then consider the risk allocation problem for convex risk measures ϱi. In general the optimal risk allocation problem is well defined only under an equilibrium condition. This condition can be characterized by the existence of a common scenario measure. We formulate ameaningful modification of the optimal risk allocation problem also formarkets without assuming the equilibrium condition and characterize optimal solutions. The basic idea is to restrict the class of admissible allocations in a proper way.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2006-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1524/stnd.2006.24.1.153","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66892889","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}
引用次数: 9
Editorial preface 编辑前言
IF 1.5
Statistics & Risk Modeling Pub Date : 2006-07-01 DOI: 10.1524/stnd.2006.24.1.iii
L. Rüschendorf
{"title":"Editorial preface","authors":"L. Rüschendorf","doi":"10.1524/stnd.2006.24.1.iii","DOIUrl":"https://doi.org/10.1524/stnd.2006.24.1.iii","url":null,"abstract":"","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2006-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66893298","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}
引用次数: 0
Law invariant concave utility functions and optimization problems with monotonicity and comonotonicity constraints 律不变凹效用函数与单调与共单调约束的优化问题
IF 1.5
Statistics & Risk Modeling Pub Date : 2006-07-01 DOI: 10.1524/STND.2006.24.1.127
G. Carlier, R. Dana
{"title":"Law invariant concave utility functions and optimization problems with monotonicity and comonotonicity constraints","authors":"G. Carlier, R. Dana","doi":"10.1524/STND.2006.24.1.127","DOIUrl":"https://doi.org/10.1524/STND.2006.24.1.127","url":null,"abstract":"SUMMARY This paper considers a class of one dimensional calculus of variations problems with monotonicity and comonotonicity constraints arising in economic and financial models where law invariant concave criteria (or law invariant convex measures of risk) are used. Existence solutions, optimality conditions, sufficient conditions for the regularity of solutions are established. Applications to risk sharing with convex comonotone law invariant risk measures or with robust utilities are given.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2006-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1524/STND.2006.24.1.127","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66892851","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}
引用次数: 42
Dilatation monotone and comonotonic additive risk measures represented as Choquet integrals 扩张单调和共单调加性风险测度用Choquet积分表示
IF 1.5
Statistics & Risk Modeling Pub Date : 2006-07-01 DOI: 10.1524/STND.2006.24.1.27
P. Grigoriev, Johannes Leitner
{"title":"Dilatation monotone and comonotonic additive risk measures represented as Choquet integrals","authors":"P. Grigoriev, Johannes Leitner","doi":"10.1524/STND.2006.24.1.27","DOIUrl":"https://doi.org/10.1524/STND.2006.24.1.27","url":null,"abstract":"SUMMARY The purpose of our paper is to link some results on the Choquet integrals with the theory of coherent risk measures. Using this link we establish some properties of dilatation monotone and comonotonic coherent measures of risk. In particular it is shown that on an atomless probability space dilatation monotone and comonotonic additive coherent risk measures have to be law invariant.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2006-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1524/STND.2006.24.1.27","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66892673","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}
引用次数: 5
Law invariant convex risk measures for portfolio vectors 投资组合向量的律不变凸风险测度
IF 1.5
Statistics & Risk Modeling Pub Date : 2006-07-01 DOI: 10.1524/stnd.2006.24.1.97
L. Rüschendorf
{"title":"Law invariant convex risk measures for portfolio vectors","authors":"L. Rüschendorf","doi":"10.1524/stnd.2006.24.1.97","DOIUrl":"https://doi.org/10.1524/stnd.2006.24.1.97","url":null,"abstract":"SUMMARY The class of all lawinvariant, convex risk measures for portfolio vectors is characterized. The building blocks of this class are shown to be formed by the maximal correlation risk measures. We further introduce some classes of multivariate distortion risk measures and relate them to multivariate quantile functionals and to an extension of the average value at risk measure.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2006-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1524/stnd.2006.24.1.97","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66892517","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}
引用次数: 2
Risk measurement with equivalent utility principles 用等效效用原则进行风险度量
IF 1.5
Statistics & Risk Modeling Pub Date : 2006-03-16 DOI: 10.2139/ssrn.880007
M. Denuit, Jan Dhaene, M. Goovaerts, R. Kaas, R. Laeven
{"title":"Risk measurement with equivalent utility principles","authors":"M. Denuit, Jan Dhaene, M. Goovaerts, R. Kaas, R. Laeven","doi":"10.2139/ssrn.880007","DOIUrl":"https://doi.org/10.2139/ssrn.880007","url":null,"abstract":"SUMMARY Risk measures have been studied for several decades in the actuarial literature, where they appeared under the guise of premium calculation principles. Risk measures and properties that risk measures should satisfy have recently received considerable attention in the financial mathematics literature. Mathematically, a risk measure is a mapping from a class of random variables to the real line. Economically, a risk measure should capture the preferences of the decision-maker. This paper complements the study initiated in Denuit, Dhaene & Van Wouwe (1999) and considers several theories for decision under uncertainty: the classical expected utility paradigm, Yaari's dual approach, maximin expected utility theory, Choquet expected utility theory and Quiggin's rank-dependent utility theory. Building on the actuarial equivalent utility pricing principle, broad classes of risk measures are generated, of which most classical risk measures appear to be particular cases. This approach shows that most risk measures studied recently in the financial mathematics literature disregard the utility concept (i.e., correspond to linear utilities), restricting their applicability. Some alternatives proposed in the literature are discussed.","PeriodicalId":44159,"journal":{"name":"Statistics & Risk Modeling","volume":null,"pages":null},"PeriodicalIF":1.5,"publicationDate":"2006-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67852289","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}
引用次数: 73
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