翻訳と辞書 Words near each other ・ Ruimveldt Riots (1905) ・ Ruin (album) ・ Ruin (publishing house) ・ Ruin a Good Time ・ Ruin Academy ・ Ruin Arch ・ Ruin Arm ・ Ruin at Daphne ・ Ruin Explorers ・ Ruin Island ・ Ruin Jonny's Bar Mitzvah ・ Ruin marble ・ Ruin Rural District ・ Ruin Tan Arash Hospital, Tehran ・ Ruin the Memory ・ Ruin theory ・ Ruin Tower ・ Ruin value ・ Ruin, Iran ・ Ruin/Renewal ・ Ruina montium ・ Ruinart ・ Ruinart (Champagne) ・ Ruinas ・ Ruination ・ Ruination (album) ・ Ruination (Transformers) ・ Ruinaulta ・ Ruine ・ Ruine Diepoldsburg Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Ruin theory ： ウィキペディア英語版 Ruin theory In actuarial science and applied probability ruin theory (sometimes risk theory collective risk theory) uses mathematical models to describe an insurer's vulnerability to insolvency/ruin. In such models key quantities of interest are the probability of ruin, distribution of surplus immediately prior to ruin and deficit at time of ruin. ==Classical model== The theoretical foundation of ruin theory, known as the Cramér–Lundberg model (or classical compound-Poisson risk model, classical risk process or Poisson risk process) was introduced in 1903 by the Swedish actuary Filip Lundberg.〔Lundberg, F. (1903) Approximerad Framställning av Sannolikehetsfunktionen, Återförsäkering av Kollektivrisker, Almqvist & Wiksell, Uppsala.〕 Lundberg's work was republished in the 1930s by Harald Cramér. The model describes an insurance company who experiences two opposing cash flows: incoming cash premiums and outgoing claims. Premiums arrive a constant rate ''c'' > 0 from customers and claims arrive according to a Poisson process with intensity ''λ'' and are independent and identically distributed non-negative random variables with distribution ''F'' and mean ''μ'' (they form a compound Poisson process). So for an insurer who starts with initial surplus ''x'', :$X\_t\; =\; x\; +\; ct\; -\; \backslash sum\_^\; \backslash xi\_i\; \backslash quad\; \backslash text\; \backslash geq\; 0.$ The central object of the model is to investigate the probability that the insurer's surplus level eventually falls below zero (making the firm bankrupt). This quantity, called the probability of ultimate ruin, is defined as :$\backslash psi(x)=\backslash mathbb^x\backslash$ where the time of ruin is $\backslash scriptstyle\; \backslash tau=\backslash inf\backslash$ with the convention that $\backslash scriptstyle\; \backslash inf\backslash varnothing=\backslash infty$. This can be computed exactly using the Pollaczek–Khinchine formula as (the ruin function here is equivalent to the tail function of the stationary distribution of waiting time in an M/G/1 queue) :$\backslash psi(x)=\backslash left(1-\backslash frac\backslash right)\; \backslash sum\_^\backslash infty\; \backslash left(\backslash frac\backslash right)^n\; (1-F^\_l(x))$ where $\backslash scriptstyle\; F^\_l(x)$ is the transform of the tail distribution of ''F'', :$F\_l(x)\; =\; \backslash frac\; \backslash int\_0^x\; \backslash left(1-F(u)\backslash right)\; \backslash textu.$ In the case where the claim sizes are exponentially distributed, this simplifies to〔 :$\backslash psi(x)\; =\; \backslash frace^-\backslash frac\backslash right)x\}.$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Ruin theory」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.