{"product_id":"life-insurance-theory-actuarial-perspectives-9781441951892","title":"Life Insurance Theory: Actuarial Perspectives","description":"\u003cp\u003e • Author(s): F. Etienne de Vylder\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Insurance - Life\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book is different from all other books on Life Insurance by at least one of the following characteristics 1-4. 1. The treatment of life insurances at three different levels: time-capital, present value and price level. We call time-capital any distribution of a capital over time: (*) is the time-capital with amounts Cl,, ..., C at moments Tl, T, ..-, T resp. N 2 N For instance, let (x) be a life at instant 0 with future lifetime X. Then the whole oO oO life insurance A is the time-capital (I, X). The whole life annuity ä is the x x time-capital (1,0) + (1,1) + (1,2) + ... + (I, 'X), where 'X is the integer part ofX. The present value at 0 of time-capital (*) is the random variable T1 T TN Cl V + v, + ... + CNV . (**) In particular, the present value ofA 00 and ä 00 is x x 0 0 2 A = and ä = 1 + v + v + ... + v'X resp. x x The price (or premium) of a time-capital is the expectation of its present value. In particular, the price ofA 00 and äx 00 is x 2 A = E( ) and ä = E(I + v + v + ... + v'X) resp.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45281000325271,"sku":"9781441951892","price":10900.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9781441951892.webp?v=1769297924","url":"https:\/\/atlanticbooks.com\/products\/life-insurance-theory-actuarial-perspectives-9781441951892","provider":"Atlantic Books","version":"1.0","type":"link"}