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For example, a maximal surcharge and monotonicity of coefficient can be desirable. Moreover, our approach can handle total losses, which are based on arbitrary loss distributions, possibly decomposed into several classes, e.g., small and large or property and bodily injury. Various costs and loadings can be also incorporated into the tariff rates. We propose optimization problems for rate estimation which enable hedging against expected losses and taking into account a prescribed loss ratio and other business requirements. Moreover, we introduce stochastic programming problems with reliability type constraints which take into account individual risk of each rate cell or collective risk. In the numerical study, we apply the approaches to Motor Third Party Liability (MTPL) policies.<\/jats:p>","DOI":"10.1142\/s0217595914500328","type":"journal-article","created":{"date-parts":[[2014,7,15]],"date-time":"2014-07-15T02:01:56Z","timestamp":1405389716000},"page":"1450032","source":"Crossref","is-referenced-by-count":8,"title":["Optimization Approaches to Multiplicative Tariff of Rates Estimation in Non-Life Insurance"],"prefix":"10.1142","volume":"31","author":[{"given":"Martin","family":"Branda","sequence":"first","affiliation":[{"name":"Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics, Charles University in Prague, Sokolovsk\u00e1 83, 18600 Prague, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2014,10,23]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2006.02.013"},{"key":"rf2","first-page":"69","volume":"73","author":"Bertocchi M.","year":"2013","journal-title":"Far East Journal of Mathematical Sciences"},{"key":"rf3","first-page":"105","volume":"48","author":"Branda M.","year":"2012","journal-title":"Kybernetika"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/j.orl.2012.01.002"},{"key":"rf5","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1080\/02331934.2011.587007","volume":"61","author":"Branda M.","year":"2012","journal-title":"Optimization: A Journal of Mathematical Programming and Operations Research"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1007\/s00186-013-0428-7"},{"key":"rf8","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1080\/01621459.1993.10594284","volume":"88","author":"Breslow N. 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