Actuarial principles of the cotton insurance in Uzbekistan

Transcription

1 Actuaral prcples of the cotto surace Uzeksta Topc : Rsk evaluato Shamsuddov Bakhodr The Tashket rach of Russa ecoomc academy, the departmet of hgher mathematcs ad formato techology 763, Uzekstasky street 49-7, Tashket, Uzeksta tel.:(998-7) fax: (998 7) 3 6 or shams964@ramler.ru Astract: The ref aalyss of moder state of crop surace Uzeksta s made. A dyamcs of a loss cost several regos of Uzeksta s show. Two methods of premum rate calculatos are revewed. The mx of these methods s offered for calculato of premum rate. Keywords: a actual producto hstory, a loss cost, a et-premum, a premum rate. Agrcultural maufacture plays a mportat role ecoomy of Uzeksta, accoutg for 5 percet of gross domestc product (GDP), 6 percet of foreg exchage eargs, ad 45 percet of employmet. By far the most mportat crop s cotto. The sow lad uder cotto s,388 mllo hectares. It s 38 % from all arale lad. Uzeksta raks as the world's ffth largest producer of cotto, wch aloe accouts for aout 5 percet of export eargs. The surace dustry Uzeksta s at a early stage of developmet. The rato of premums to GDP s aout,5 percet. As of May 3, the surace dustry comprsed 9 regstered surace compaes. There s oly oe surace compay that provdes agrculture surace servce, Uzagrosugurta State jot stock surace compay. The compay provdes all rsks surace related to agrculture. The preset paper s devoted to research of tarff poltcs of the Usagrosuguta compay the feld of cotto surace. The crop surace tll 997 was madatory. The premum rates were estalshed y way of -,5 percets wthout depedece o geographcal ad clmatc codtos. The trasto to volutary crop surace has led to dfferetato ad sharp crease of the premum rates all regos of Uzeksta. Ad the crease of premum rates has led to a decrease of demad to ths surace servce. I 5,66 percet cotto plated areas were sured.

2 The cotto surace s cludes such rsks, as a drought, a hurrcae, a cold, a halstoes, a dowpour, a flood, a wreckers, a ologcal llesses - the umer of such rsks s 8. A polcyholder estalshes a actual producto hstory (APH) yeld ased o the grower's actual producto records for 5 years. If the grower does ot have 5 years of producto records, a APH yeld ca e ased o as lttle as 3 years of yeld data. Coverage level s 5%. Lalty = Prce Guaratee * APH yeld * Coverage level Premum = Lalty * Premum rate Idemty = Lalty Market prce of actual yeld The crop surace s a uproftale kd of actvty. Therefore premum rates have hgh meags. I Uzeksta premums are ot susdzed, ut surace demtes are susdzed. I ths coecto, some regos of repulc, rsky for agrculture, the Uzagrosugurta compay s compelled to reder surace servces y the surace premum rates adequately to losses. Fgure shows a comparso of average loss cost wth a premum rate 5 regos of Uzeksta - Carakalpaksta (I), Kashkadarya (II), Namaga (III), Surkhadarya (IV) ad Tashket (V). Fgure shows the dyamcs of loss cost these regos ad Repulc of Uzeksta (VI) for 998- years.,35,3,5,,5,,5 I II III IV V Loss rato Premum rate Fgure.

3 ,6,5,4 Loss rato,3,, Crop year I II III IV V VI Fgure. It s well kow that the premum rate s calculated o statstcs of a loss cost for a certa perod (usually, for 5- years). There exst methods of calculato of the premum rate, appled y the Uzagrosugurta compay. Method s ased o a average loss cost. Method s ased o a estmato of future value of a loss cost. The ref descrpto of these methods. For coveece we eter the followg desgatos: S, S,, S - the total laltes of compay o some kd of crop surace for years, accordgly; Q, Q,, Q - the total demtes for years, accordgly. The szes of the loss cost for year -,,,, a aual average loss cost for years ad a root-mea-square devato σ are calculated o the ass of ths statstcs: Q =, = S =, ( ) = σ =, =,,, () The et-premum rate cossts of two parts - asc ad rsk compoets. The asc compoet of the et-premum rate s equal to T о = () The rsk compoet of the et-premum rate s equal to Tr = β(γ,) σ

4 where β(γ,) the quatle of the Studet s dstruto wth parameters (guaratee of safety) ad (umer of degrees of freedom). Thus et premum s equal to T = +β(γ,) σ The secod method s appled f there exsts lear tred dyamcs of loss cost We fd a estmato of the future loss cost o the ass of statstcs,,, ad usg the formula of lear approxmato. The model of lear approxmato has the followg formula: where =a +a, =,,,. (3) - leveled parameter of loss cost, a, a - parameters of lear tred. The parameters of lear tred are defed o a method of the least squares, that s reduced to the decso of system of two lear equatos: a a + a = + a = The asc compoet of the et-premum s defed as: (4) Т ~ o = п+ =a +a (+) (5) The et-premum s equal to where ( ) ~ = = σ Т ~ = + +β(γ,) ~ σ (7) I fgure 3 s show the asc compoet of the et-premum, that s calculated o these methods. Rego T o (method ) T o (method ) I,3,8 II,, III,3, IV,7,3 V,5, Fgure 3.

5 Great dfferece these calculatos leads to dout of expedecy of applyg such methods ths partcular case. The drawack of method s, that the character of chage of dyamcs of the loss cost s ot take to accout. From the fgure t s ovous, that all regos the loss cost has decreased strogly. A depedece o the real statstcal data of loss cost o tme s far from eg lear. It also explas of applcalty of method ths case. Calculatg the premum rate t s ecessary to take to cosderato the crop surace peculartes. The crop productvty depeds frst of all o clmatc codtos. The cotract of surace, as a rule, s sged efore the cotto sowg term s eded. I Uzeksta the sowg works of cotto usually eg Aprl. By ths tme t wll e possle to predct clmatc codtos durg for producto perod of a cotto (May - Novemer). It s possle to expect estmatos of loss cost o the ass of ths forecasts. We offer a mx of two aove-stated methods as a method of accout of the asc part of the et-tarff: Τ = α +( α) +, α Parameter α gets out depedg o. forecasts for clmatc codtos durg the producto perod;. the actual producto hstory. Blography. Sal V., Alamskaya L., Kovalev O. A mathematc-ecoomc methodology of geeral surace s aalyss.( Russa). Moscow, ANKIL, 997. Shamsuddov B.R. Actuaral methods of a premum rate's calculato. I the Proceedgs of the semar «The moder state ad prospects of developmet of surace usess the Repulc of Uzeksta», Tashket,, July, page The asc dcators of Socal ad Ecoomc Developmet of the Repulc of Uzeksta. Statstcal dgest. Tashket, 3.