"RIV/00216275:25410/14:39898355" . . "Ruin probability in reinsurance"@en . . "Scientific Papers of the University of Pardubice, Series D, Faculty of Economics and Administration" . . "P(EE2.3.30.0058)" . "Ruin probability in reinsurance"@en . "[70D017E6579A]" . . "V pojistn\u00E9 matematice teorie ruinov\u00E1n\u00ED vyu\u017E\u00EDv\u00E1 matematick\u00E9 modely pro popis zranitelnosti pojistitele ke krachu. Teoretick\u00E9 z\u00E1klady teorie ruinov\u00E1n\u00ED popisuje poji\u0161\u0165ovac\u00ED spole\u010Dnost, kter\u00E1 za\u017E\u00EDv\u00E1 dv\u011B protich\u016Fdn\u00E9 pen\u011B\u017En\u00ED toky: p\u0159\u00EDchoz\u00ED pen\u011B\u017En\u00ED pr\u00E9mie a odchoz\u00EDch pojistn\u00E9 pln\u011Bn\u00ED. P\u0159ebytek pojistitele je n\u00E1hodn\u00E1 prom\u011Bnn\u00E1, proto\u017Ee jeho hodnota z\u00E1vis\u00ED na pojistn\u00E9 a pojistn\u00E1 pln\u011Bn\u00ED. Poji\u0161\u0165ovna po\u017Eaduje, aby pravd\u011Bpodobnost krachu tak mal\u00E9, jak je to mo\u017En\u00E9, nebo alespo\u0148 pod p\u0159edem stanovenou mez. Lundbergova nerovnost poskytuje horn\u00ED mez pro pravd\u011Bpodobnost krachu v nekone\u010Dn\u00E9m \u010Dase a je jedn\u00EDm z nejzn\u00E1m\u011Bj\u0161\u00EDch v\u00FDsledk\u016F v teorii ruinov\u00E1n\u00ED. Jednou z mo\u017Enost\u00ED pro pojistitele, kter\u00FD chce sn\u00ED\u017Eit pravd\u011Bpodobnost krachu je prov\u00E9st zaji\u0161t\u011Bn\u00ED. Budeme zva\u017Eovat dva druhy zaji\u0161t\u011Bn\u00ED: proporcion\u00E1ln\u00ED a zaji\u0161t\u011Bn\u00ED \u0161kodn\u00EDho nadm\u011Brku. Mohli bychom uva\u017Eovat o zaji\u0161t\u011Bn\u00ED, kter\u00E9 je optim\u00E1ln\u00ED (z poji\u0161\u0165ovny hlediska), pokud minimalizuje pravd\u011Bpodobnost krachu. C\u00EDlem t\u00E9to pr\u00E1ce je uk\u00E1zat, jak\u00FD vliv maj\u00ED zm\u011Bny faktoru zat\u00ED\u017Een\u00ED pojistn\u00E9ho (pou\u017E\u00EDvan\u00E9 pojistitelem a zajistitelem), na pravd\u011Bpodobnost krachu pro oba druhy zaji\u0161t\u011Bn\u00ED. Najdeme tak\u00E9 optim\u00E1ln\u00ED typ zaji\u0161t\u011Bn\u00ED za ur\u010Dit\u00FDch podm\u00EDnek."@cs . "Pravd\u011Bpodobnost ruinov\u00E1n\u00ED p\u0159i zaji\u0161t\u011Bn\u00ED"@cs . . . "Gogola, J\u00E1n" . "V pojistn\u00E9 matematice teorie ruinov\u00E1n\u00ED vyu\u017E\u00EDv\u00E1 matematick\u00E9 modely pro popis zranitelnosti pojistitele ke krachu. Teoretick\u00E9 z\u00E1klady teorie ruinov\u00E1n\u00ED popisuje poji\u0161\u0165ovac\u00ED spole\u010Dnost, kter\u00E1 za\u017E\u00EDv\u00E1 dv\u011B protich\u016Fdn\u00E9 pen\u011B\u017En\u00ED toky: p\u0159\u00EDchoz\u00ED pen\u011B\u017En\u00ED pr\u00E9mie a odchoz\u00EDch pojistn\u00E9 pln\u011Bn\u00ED. P\u0159ebytek pojistitele je n\u00E1hodn\u00E1 prom\u011Bnn\u00E1, proto\u017Ee jeho hodnota z\u00E1vis\u00ED na pojistn\u00E9 a pojistn\u00E1 pln\u011Bn\u00ED. Poji\u0161\u0165ovna po\u017Eaduje, aby pravd\u011Bpodobnost krachu tak mal\u00E9, jak je to mo\u017En\u00E9, nebo alespo\u0148 pod p\u0159edem stanovenou mez. Lundbergova nerovnost poskytuje horn\u00ED mez pro pravd\u011Bpodobnost krachu v nekone\u010Dn\u00E9m \u010Dase a je jedn\u00EDm z nejzn\u00E1m\u011Bj\u0161\u00EDch v\u00FDsledk\u016F v teorii ruinov\u00E1n\u00ED. Jednou z mo\u017Enost\u00ED pro pojistitele, kter\u00FD chce sn\u00ED\u017Eit pravd\u011Bpodobnost krachu je prov\u00E9st zaji\u0161t\u011Bn\u00ED. Budeme zva\u017Eovat dva druhy zaji\u0161t\u011Bn\u00ED: proporcion\u00E1ln\u00ED a zaji\u0161t\u011Bn\u00ED \u0161kodn\u00EDho nadm\u011Brku. Mohli bychom uva\u017Eovat o zaji\u0161t\u011Bn\u00ED, kter\u00E9 je optim\u00E1ln\u00ED (z poji\u0161\u0165ovny hlediska), pokud minimalizuje pravd\u011Bpodobnost krachu. C\u00EDlem t\u00E9to pr\u00E1ce je uk\u00E1zat, jak\u00FD vliv maj\u00ED zm\u011Bny faktoru zat\u00ED\u017Een\u00ED pojistn\u00E9ho (pou\u017E\u00EDvan\u00E9 pojistitelem a zajistitelem), na pravd\u011Bpodobnost krachu pro oba druhy zaji\u0161t\u011Bn\u00ED. Najdeme tak\u00E9 optim\u00E1ln\u00ED typ zaji\u0161t\u011Bn\u00ED za ur\u010Dit\u00FDch podm\u00EDnek." . . "Pravd\u011Bpodobnost ruinov\u00E1n\u00ED p\u0159i zaji\u0161t\u011Bn\u00ED" . . "Pravd\u011Bpodobnost ruinov\u00E1n\u00ED p\u0159i zaji\u0161t\u011Bn\u00ED"@cs . "25410" . "1211-555X" . . "30" . . "1"^^ . "38548" . . "RIV/00216275:25410/14:39898355!RIV15-MSM-25410___" . "Pravd\u011Bpodobnost ruinov\u00E1n\u00ED p\u0159i zaji\u0161t\u011Bn\u00ED" . "CZ - \u010Cesk\u00E1 republika" . . "In actuarial science ruin theory uses mathematical models to describe an insurer's vulnerability to ruin. Theoretical foundation of ruin theory describes an insurance company who experiences two opposing cash flows: incoming cash premiums and outgoing claims. The insurer's surplus at any future time is a random variable since its value depends on premiums and claims. The insurer want to keep the probability of ruin as small as possible, or at least below a predetermined bound. Lundberg's inequality provides an upper bound for the probability of ruin in infinite time and is one of the most famous results in ruin theory. One of the options for an insurer who wishes to reduce the probability of ruin is to effect reinsurance. We shall consider two kinds of reinsurance arrangement: proportional and excess of loss reinsurance. We could consider a reinsurance arrangement (from an insurer point of view) to be optimal if it minimizes the probability of ruin. The goal of this paper is to illustrate how changes in the premium loading factor (used by insurer and reinsurer) affect the probability of ruin in both kind of reinsurance. We find also the optimal type of reinsurance under certain conditions."@en . "1"^^ . "1/2014" . . . . . "Reinsurance, Ruin theory, Proportional and Excess of Loss Reinsurance, Adjustment coefficient, Retention level, Compound Poisson process,"@en . . . "11"^^ .