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- W2269708002 abstract "This book is about heavy-tailed random variables and the phenomena they induce to mathematical models. It has become clear that the classical models employing light-tailed variables have an inherent tendency to underestimate the magnitude of extremal events. Recent developments in the financial world (financial crises) suggest that such shortcomings are not merely theoretical curiosities, but game-changing phenomena that can solely determine the fate of an agent. To overcome the obstacles set by the classical lines of thought an agent must consider ways to improve the way risk is modelled and assessed. The book proposes two ways to do this. Firstly, the existing models are reconfigured to include the effects of different types of risks. Secondly, heavy-tailed effects such as the principle of a single big jump are made more transparent by a detailed investigation. The mathematical theory of this book is based on the theory of random walks and their generalisations. Special attention is paid to randomly weighted random walks and randomly stopped random walks that are commonly encountered in the field of insurance mathematics.%%%%Nykyaikaiset taloudelliset toimijat ovat mukana liiketoimissa, joista syntyvat tappiot voivat ylittaa moninkertaisesti kaytettavissa olevat varat. Tama altistaa pankit ja vakuutuslaitokset suurille riskeille. Matemaattisessa mielessa aarimmaisia riskeja voidaan mallintaa kayttamalla satunnaismuuttujia, joiden hantafunktiot vahenevat hitaasti. Hitaasti vahenevat hantafunktiot mahdollistavat suuret realisaatiot suhteellisen suurella todennakoisyydella. Satunnaismuuttujia, joiden hantafunktio vahenee riittavan hitaasti, kutsutaan paksuhantaisiksi. Vaitoskirja kasittelee sita, millaisia vaikutuksia paksuhantaisilla satunnaismuuttujilla on matemaattisissa malleissa ja millaisia ilmioita paksuhantaiset satunnaismuuttujat tuottavat. Vaikutuksia tutkitaan erilaisissa diskreeteissa malleissa, jotka perustuvat satunnaiskulkuun tai sen yleistyksiin. Erityista huomiota kiinnitetaan vakuutusmatematiikassa esiintyviin satunnaisiin diskonttausmalleihin ja satunnaisesti pysaytettyihin summiin. Lisaksi paksuhantaisille malleille tyypillinen yhden suuren hypyn periaate eristetaan yksinkertaisimpaan mahdolliseen viitekehykseen." @default.
- W2269708002 created "2016-06-24" @default.
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- W2269708002 date "2016-02-20" @default.
- W2269708002 modified "2023-09-27" @default.
- W2269708002 title "On Heavy-tailed Risks with Applications to Insurance and Finance" @default.
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