{"title":"On a Theory that Supports Stable Pensions","authors":"K. Aase","doi":"10.1142/9781786341952_0006","DOIUrl":"https://doi.org/10.1142/9781786341952_0006","url":null,"abstract":"","PeriodicalId":372632,"journal":{"name":"Risk and Stochastics","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115501020","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":"Maybe You Chose the Wrong Niche in Life, Norberg Ragnar","authors":"R. Norberg","doi":"10.1142/9781786341952_0002","DOIUrl":"https://doi.org/10.1142/9781786341952_0002","url":null,"abstract":"","PeriodicalId":372632,"journal":{"name":"Risk and Stochastics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130421414","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":"Dividend Payment with Ruin Constraint","authors":"C. Hipp","doi":"10.1142/9781786341952_0003","DOIUrl":"https://doi.org/10.1142/9781786341952_0003","url":null,"abstract":"","PeriodicalId":372632,"journal":{"name":"Risk and Stochastics","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117284402","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":"The Work of Ragnar Norberg","authors":"N. Bingham","doi":"10.1142/9781786341952_0001","DOIUrl":"https://doi.org/10.1142/9781786341952_0001","url":null,"abstract":"","PeriodicalId":372632,"journal":{"name":"Risk and Stochastics","volume":"103 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117178022","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":"Remark on the Paper “Entropic Value-at-Risk: A New Coherent Risk Measure” by Amir Ahmadi-Javid, J. Optim. Theory Appl., 155(3) (2001) 1105–1123","authors":"F. Delbaen","doi":"10.1142/9781786341952_0009","DOIUrl":"https://doi.org/10.1142/9781786341952_0009","url":null,"abstract":"","PeriodicalId":372632,"journal":{"name":"Risk and Stochastics","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127528156","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":"The Pedestrian’s Guide to Local Time","authors":"Tomas Bjork","doi":"10.1142/9781786341952_0005","DOIUrl":"https://doi.org/10.1142/9781786341952_0005","url":null,"abstract":"These notes contains an introduction to the theory of Brownian and diffusion local time, as well as its relations to the Tanaka Formula, the extended Ito-Tanaka formula for convex functions, the running maximum process, and the theory of regulated stochastic differential equations. The main part of the exposition is very pedestrian in the sense that there is a considerable number of intuitive arguments, including the use of the Dirac delta function, rather than formal proofs. For completeness sake we have, however, also added a section where we present the formal theory and give full proofs of the most important results. In the appendices we briefly review the necessary stochastic analysis for continuous semimartingales. I am very grateful to Mariana Khapko for valuable comments, and for giving me the necessary motivation to write this paper. Many thanks are also due to Boualem Djehiche for valuable comments and suggestions.","PeriodicalId":372632,"journal":{"name":"Risk and Stochastics","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121141169","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":"Orthonormal Polynomial Expansions and Lognormal Sum Densities","authors":"S. Asmussen, P. Goffard, P. Laub","doi":"10.1142/9781786341952_0008","DOIUrl":"https://doi.org/10.1142/9781786341952_0008","url":null,"abstract":"Approximations for an unknown density $g$ in terms of a reference density $f_nu$ and its associated orthonormal polynomials are discussed. The main application is the approximation of the density $f$ of a sum $S$ of lognormals which may have different variances or be dependent. In this setting, $g$ may be $f$ itself or a transformed density, in particular that of $log S$ or an exponentially tilted density. Choices of reference densities $f_nu$ that are considered include normal, gamma and lognormal densities. For the lognormal case, the orthonormal polynomials are found in closed form and it is shown that they are not dense in $L_2(f_nu)$, a result that is closely related to the lognormal distribution not being determined by its moments and provides a warning to the most obvious choice of taking $f_nu$ as lognormal. Numerical examples are presented and comparisons are made to established approaches such as the Fenton--Wilkinson method and skew-normal approximations. Also extensions to density estimation for statistical data sets and non-Gaussian copulas are outlined.","PeriodicalId":372632,"journal":{"name":"Risk and Stochastics","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114849542","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}