{"title":"投资组合的共同因果条件风险中性 PDE","authors":"Alejandro Rodriguez Dominguez","doi":"arxiv-2401.00949","DOIUrl":null,"url":null,"abstract":"Portfolio's optimal drivers for diversification are common causes of the\nconstituents' correlations. A closed-form formula for the conditional\nprobability of the portfolio given its optimal common drivers is presented,\nwith each pair constituent-common driver joint distribution modelled by\nGaussian copulas. A conditional risk-neutral PDE is obtained for this\nconditional probability as a system of copulas' PDEs, allowing for dynamical\nrisk management of a portfolio as shown in the experiments. Implied conditional\nportfolio volatilities and implied weights are new risk metrics that can be\ndynamically monitored from the PDEs or obtained from their solution.","PeriodicalId":501045,"journal":{"name":"arXiv - QuantFin - Portfolio Management","volume":"28 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Portfolio's Common Causal Conditional Risk-neutral PDE\",\"authors\":\"Alejandro Rodriguez Dominguez\",\"doi\":\"arxiv-2401.00949\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Portfolio's optimal drivers for diversification are common causes of the\\nconstituents' correlations. A closed-form formula for the conditional\\nprobability of the portfolio given its optimal common drivers is presented,\\nwith each pair constituent-common driver joint distribution modelled by\\nGaussian copulas. A conditional risk-neutral PDE is obtained for this\\nconditional probability as a system of copulas' PDEs, allowing for dynamical\\nrisk management of a portfolio as shown in the experiments. Implied conditional\\nportfolio volatilities and implied weights are new risk metrics that can be\\ndynamically monitored from the PDEs or obtained from their solution.\",\"PeriodicalId\":501045,\"journal\":{\"name\":\"arXiv - QuantFin - Portfolio Management\",\"volume\":\"28 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - QuantFin - Portfolio Management\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2401.00949\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - QuantFin - Portfolio Management","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2401.00949","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Portfolio's Common Causal Conditional Risk-neutral PDE
Portfolio's optimal drivers for diversification are common causes of the
constituents' correlations. A closed-form formula for the conditional
probability of the portfolio given its optimal common drivers is presented,
with each pair constituent-common driver joint distribution modelled by
Gaussian copulas. A conditional risk-neutral PDE is obtained for this
conditional probability as a system of copulas' PDEs, allowing for dynamical
risk management of a portfolio as shown in the experiments. Implied conditional
portfolio volatilities and implied weights are new risk metrics that can be
dynamically monitored from the PDEs or obtained from their solution.
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