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Strahuvannya - Osadets SS

18.3. Viznachennya tariffs for contracts of fatal insurance

Класичний підхід до визначення тарифів . Under the contracts of a pseudo insurance, it is possible to negotiate insurance in full, but not by insurance contracts. Negotiation of a pagan insanity is characterized by a short term with a contract - for up to one rock. Specificity is viznacha character of the special arrangement of insurance tariffs for such contracts:

• Calculating the value of the insurance premium;
• Не враховуться можмивий інвестиційний прибуток від розміщення тимчасово вільних коштів insurance reservesів із цих видів страхування.

At rozraunku net-premiyny for contracts of fatal insurance in vvazhayut, sho rozmіr N razvovoe netto-premiіi virazhaye ekvіvalentnost zobov'azan insavika ta insuranceu i igroprotsiyna before insurance Sumi S :

,

Де кефіцієнт пропорційності Т nazivayut net-tariff , abo net-rate .

Gross-premium B , abso simple insurance premium, proportional net-premi N :

,

Де коефіцієнт пропорційност a (a> 1) містить a part f навантаження (адміністративні витрати, комісійні, плановий прибуток страховика) і визначається співвідношенням

.

For viznachennya structure netto-tariff for the contract of fatal insurance is rozglyanemo hipotitichny vipadok, if vidoma all neobhydna for rozraunkіv informatsiia.

Applied . Pripustimo, scho when carried out insurance of the viznachenogo risiku (napriklad, maynovu insurance of everyday life in the verse) a stretch of a fictitious promuyku hour D t (napriklad, one rock) insured planned:

• Insurance for n ( n = 1, 2, ...) contracts with insured sums S 1, S 2, S 3, ..., Sn ;
• Nastaniya zi tsimi contracts m insurance vipadkіv zi insurance payments , , , ..., .

Viznachimo rozmіr net-tariff for insured riziku, a kind of Відповідав bi taken zobov'yаnnyam insavіkі з nazvanih vidіv іnhavannya.

In a detailed vipadku net-tariff can be distinguished on the basis of the principle of exclusion of zobov'azan insurance policy and insurance. Zobov'yazaniya insurvician dorivnemy sumy insured vidshchoduvan

,

А зобов'язання страхувальників - сумі подамих нетто-премій

De T 0 is a net tariff, a kind of potrebno viznachiti. The value of T 0 in the given application can be estimated from the balance of the zobov'azan insurance of those insured:

,

Abo

.

In the case of the balance sheet, the viconate is gradually cumbersome for insurance contracts, replacing the residual part of the mn :

,

But gave, having entered the meaning - mid-term insurance vyplaty that meaning - average insurance sum for one dogovir

, ,

Go to sleep

,

Zvidki known shukane znachennya net-fare

.

Останню рівність записують, як правило, у вигляді

,

Toto virazhayut net-rate for insured risky through two basic parameters:

• Koefitsynt zbitkostysti for danim insurance

;

• Frequency of insurance

.

Misrepresentation of the virishuta stavlenje zavdannya i give zmogu rozrahovuvati net-rate for insured persons with a risk of deprivation in apostyriarnomu (pislyadoslidnomu) vipadku if vidoma all neobhіdna іnformatsіya, and same - vіdomі znachennya parameterіv n , m , , Abo Kzb, w . At the practical level, with the up-to-date (up to the back of the doslik), the tariffs for the winter and winter are not vidomies and vosnyas vipadkovymi doodatnymi values. Ale is a guide to the business that otriman spіvvidnoshennya majut important for valuation for perevirki i koriguvannya for the results of insurance diyalnost regularities of the regional tariffs. Same cі співвідношення vkazuyut on neobhіdnіst у діяльності кожної страхової компанії postійного спостеження та аналізу знаност параметів Kзб, w за прийнятим на страхування ризиком і дають змогу perіодично koriguvati vpernad viznachenі for this risk tariff rate.

In the case of a marginal net fee for a fatal vipack, a high-visibility model for insured vedushkudavan at a safe rate T 0 = Kzb w potrivno rozv'yati superechnits, yaka polegai in that part of the net (net-rate) mie bouti in front of an identified fictional value, and the rights of a part Vipadkova value, the value of the anchor can not be easily changed in the course of the insurer's life.

For rozv'yazannya tsієї superechnosti widly zastosuvannya nabuv method, a way to get on that, vice versa vipadkovoi magnitudes can be taken її naybіlis mozhlive іz prednavnuyu dovіrchoyu ymііrnistyu znachennya.

Such pidhid viznachaet structure net-tariff for the contract zagalnoy insurance:

,

De T 0 = M [Kzb w ] - the main part of the net-rate (mathematician of the value of insurance in sums of money insurance contracts for insignificant risks);

Tp = T 0J - Rizikova (insurance) premium to the main part of the net-tariff, yaka iz dovіrchoyu ymііrnistyu vrahovu mozhivі nezhazhinі vіdhilennya J vіdnosії zhizni viplat i іnchislyuetsya for the formula:

,

De n - kilkist contract in insurance for viznachenym rizikom, scho planuetsya;

P - імовірність nastannya insurance under the visas for the risky.

Behind the law of great numbers for great values ​​of n Vipadkov, the value of w is straightforward from the point of view of the theoretical underdelivery of insurance under the risk and p = M [ w ].

Otzhe, net-tariff with insurance premiums for the risk of retailing is given by the pre-requisite of the taxation for the formula

,

De t g is the quantile of the g-value of the normal rozpodil;

N - kilkist contract in insurance for vises a risk, scho planuetsya;

P - the value of the insured under the visas;

M [Kзб] - математичне сподівання збитковості.

The mathematician of determining the size of a Kzb for a viznachenogo riziku is practically not zmіnyuyutsya і mozhe bouti viznacheno so:

• 0,3 - in case of insecurity of unhappy vipadkivs that crook;
• 0,4 - with insurance of land transport;
• 0,5 - in case of insured persons, that lane (in the form of transport);
• 0,6 - with insurance coverage of water transport;
• 0,7 - in case of insured traffic accidents in the transport of vehicles that have the least visibility in the course of their stay, but also in the case of insurance fianosovyh rizikiv.

For calculating the net premièe for the contract, insuring the risk of contracting the net-rate multiplied by the insurance sum: N = ST .

Zauvazhimo, but the net value of the rate is stable:

• Від планинованої кількості договоів insured for viznacheniyom rizikom і зменшується з їх зростанням до математического сподівання збиків з одиниці страхової суми;
• Від значення довірчої ймовірності шуканого тарифу і зростає з наближенням цього значення до одиниці;
• Від точності вибору значення коефіцієнта збитковості.

Insurance of tariffs in the model of insurance. Introduced in a clear form of visage virazhayut klasichnyi pidhid rozraunku net-rate for insurance risk for the validity of the minimum information about the Maybutny's insurance. Якщо відомі додаткові статистичні дані about the process of insuring the insurance, mozhlive zastosuvannya більш exact methodів обчисня страхових тарифів.

For розв'язання відповідних problems to enter різні stochasticheskimі model of insurance rizikів і rozglyadayut відповідні моделі розподілу суманого розміру страхового відшкодування. Nayprostoshoyu of them є model індивідуальних ризиків , яка щодо договоів загального страхування передбачає таке:

• Kількість n нелележних між собою договоів insured fіksovana ta beforehand is identified;
• For a cutaneous contract, insure against the statistical authorities of the damage caused to him by the canvassing of Hk , de k is the ordinal number of the contract.

Zauvazhimo, scho is far from being the contract for a contract to pay insurance vishodshduvannya, the act vipadkovi magnitude Xk (insured vidshkoudavan for k- th contract) can dorivnyuvaty zero.

Obalny rozmіr insurance vіdshkoduvannya for the insurance subord, tobto rozmіr zobov'azan insurance, viznachaє suma nezolezhnih mezh vypadikikh magnitudes

.

In the case of a fatal vipadka in the case of a vikoristan model of indivisual risk, the value Bk of insurance premiums for the k- th insurance contract ( k = 1, 2, ..., n ) is deducted from the presumptive value of the insurance premiums for the insured insurer for the formula

,

De M [ Xk ] - mathematician spodivannya vidshkduvan for k- th contract insurance;

J - insurance premium is insignificant.

The basis of the extras to the value of Bk in the fatal vipadka is to enter the Sumi value M [ Xk ], yaku name the main part of the net premiè . Dodatkovu sum J M [ Xk ] name the risky (insurance) premium to the main part , yaka iz dovyrochoyu ymovirnistyu vrahovu mozhivі nezhazhiny vidhilennya vidnosnoi frequency nastannya insurance podії.

At the practice of vikorostvuyot kilka podvіv rozraunku vіdnosnoї insurance premiums for insured viznachenogo risiku:

1) з фіксованим значенням для всіх договорів страхування

,

De t g is the quantile of the g- value of the normal rozpodil;

M [ Sn ] - mathematician of the spodivaniya sumarnogo rozmіru insurance vidshchodavan;

D [ Sn ] - dispersion of the sum total of insurance insurances;

2) зі змінним значенням, пропорційним дисперсії або середньквавадратичным виіхихиленню size of insurance vідшкодування Хk for k- th contract, тобто у вигляді

, Abo , K = 1, 2, ..., n .

Zauvazhimo, scho u navedenih spivvidnoshenney numerals characteristics vipadkovyh values Xk insurance vіshkoduvannya for the k- th contract viznachayutsya zalizhno vіd nayavnії statіchnoї іnformatsії about the process of insurance coverage.

In the case, if the number of characteristics of the summed rozmiru Sn insured vidshchoduvan for insuring the risk on the pidstavi central boundary theorems, you can calculate the amount of available insurance coverage in the reserve r rozmiru r for vikonannya zobov'azan insavika zim rizikom:

,

Abo ymovirnosti rozorennya (lack of nayavnih insurance reserves):

,

De F 0 ( x ) is the integrand of the normed normal rod.

Insurance tariffs in the collective model of risk. Warehouse model rozpodilu sumarnogo rozmіru insurance vіdshoduvannya for viznacheniyom rizikom virazhaє kolektivnaya model risiku , yaka rozglyadaє not okremі contract insurance, and the entire portfolio of contracts for danim is insured by a risky and perebacha:

• Кількість n Wimog about insurances vishodshduvannya for danim rizikom on fіksovanomu promіizku hour - Vipadkova value (yak rule, with poissonivsky rozpodilom);
• The value of the last insurance policy Y 1, Y 2, ..., Y n for the portfolio of the insurance risk for which the promissory hour is to say after the values ​​of the vipadkovyh values, but the same is true for the roses;
• Vipadkov's values ​​of n , Y 1, Y 2, ..., Y n are unclosed in the joint.

The selective model of vrachovu is the possibility of a non-reusable insured under the insurance contract (insurance is important in the contracts of the insured person), it is not deprived of the identity of the client, the account of the bankruptcy agreement, the insured person, the person who is in charge of the work, Yk , k = 1, 2, ..., n Від індивідуальної моделі, дезначення відшкодувань Хk could buti zeroiovi). Sumarniy rozmіr S insured vіdshchoduvan for the insurmountable rizikom at kolektivnіy model viznachaє vipadkova suma nezalezhnih mіzh soboju vypadkovyh sizes

.

For assigning the numerical characteristics of the quantity, n, and, for, insuring against the amount of Y of an insurance insider, in a fatal vipadka, one can know the number of characteristics of the summed rozmir S insurance vishodkuvan for the insurmountable rizik in the collective model

;

.

Nyprostіshu i nayposhirenіsu model rozpodilu kіlostі іnstovyh vimog n viznachaє rozpodіl Poisson with parameter l, if

, K = 0, 1, 2, ...,

Prichomu

M [n] = D [n] = l.

In the case of the Vipadku rozpodil Vipadkovo value S name the collapsible ropodilom Poisson , and її numerals characteristics vysnachayut formulas

;

.

It is commendable that the parameter l Poisson's Poisson's generator and the integrand F ( t ) = P { Y < t } determine the value of the Vipadkaya value Y of an insurance insignia, denoted by the parameters of a collapsible rozpodil of Poisson, written in the form S ~ CP (l; F ) . Moreover, at the prompts, the parameter l is viznachaet serednyu for the portfolio kilkist insurance vimog (vimog about the payment of insurance vishkohduvannya) for oditnitsu hour (napriklad, for one pik).

In the case of insurance, it is important to realize the fact that the sum of the unoccupied vipadkovsky quantities, the skin of such a collapsible rospodil of Poisson, is also the folding rospodil of Poisson. Vikonuetsya firmzhennya:

Yakshchoo S 1, S 2, ... is a distinctly independent blow-up value, the skin of which is rozpodilen for the folded Poisson rosepod Sk ~ CP (l k ; Fk ), k = 1, 2, ..., - збіжний, then the sum S = = S 1 + S 2 + ... is also a collapsible rosepod Poisson S ~ CP (l; F ), the parametre is the same as the value of the spin

.

Stimulated by hardening to practice vikoristovuyut in such vipadkah:

• When the insurance cards are not insolvent, such insurance agents Sk , k = 1, 2, ..., m by skinning them, the collapsible rosodile Poisson Sk ~ CP (l k ; Fk ); The result of the return of the portfolio, the sum total of the insurance insurances S yakogo takozh viznachati collapsible rozpodil Poisson S ~ CP ( ; );
• At the expense of the sum of money for m rockies of insurance insecurity S for one and the same insured by a risk of unearthed richest insured scuffs Sk , k = 1, 2, ..., m , skins for which the collapsible rods of Poisson, can be invaded, Rozpodil Poisson.

In the case of a fatal vipadku with a vikoristani model of a collective risk, the B value of insurance premiums for all contracts is insured, however, that you should notify yourself of the amount of insurance premiums for vikonannya zobov'azan insurant for the formula

B = l 1 M [ Y ] (1 + J),

De M [ Y ] - mathematician of the opportunity to pay one insurance deduction;

L1 - the average for one dogovir number of insured persons for one hour;

J - insurance premium is insignificant.

The basis of the extrusions up to the value of B in the fatal vipadku is to enter the value Sumi l1 M [ Y ], yaku name the main part net-premii. Dodatkovu sumu Jl1 M [ Y ] call a risky (insurance) mark-up to the main part, yaka iz dovіrchoyu ymііrnistyu vrahovu mozvolі nezhazhі vіdhilennya vіnodnoї frequency nastannya insurance podії.

Відносна insurance extra charge for insured persons risky має фіксоване for all contracts в zinchenia і розраховується за формулою

,

De t g is the quantile of the g-value of the normal rozpodil;

M [ S ] - mathematics of the spodivaniya sumarnogo rozmіru insurance vidkshduvan;

D [ S ] - dispersion of the sum total of insured products.

MATHEMATICS spodivannya M [ Y ] one insurance vіdshkoduvannya viznachaatsya zalizhno vіd nayavnії statіchnoї іnformatsії about the process of insuring the insurance.

Serednya for one dogovir kilkost l1 insured wimogs for odinitsyu hour (for a fatal vipadku - for one rik) rozrahovuyutsya on pidstavi sreddnyoi for a portfolio kolosty l insurance vimog for oditnitsu hour (takozh - one rik):

,

De n - viznachaet kilkіst contract in the insurance portfolio, for yakogo bolo know the value of the parameter l.