Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://new.math.msu.su/department/probab/doklady/Falin_GI_Programma_podgotovki_aktuariev_ver-3.pdf Äàòà èçìåíåíèÿ: Wed Apr 1 00:23:10 2015 Äàòà èíäåêñèðîâàíèÿ: Sun Apr 10 01:56:48 2016 Êîäèðîâêà: IBM-866

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1911 Encyclopödia Britannica: The name of actuarius ... in ancient Rome, was given to the clerks who recorded the Acta Publica of the senate, and also to the officers who kept the military accounts and enforced the due fulfilment of contracts for military supplies.


16 . Oxford dictionary: actuary [aktri, -tj-] Origin: mid 16th cent. originally denoting a clerk or registrar of a court 1911 Encyclopödia Britannica: ACTUARY. ... In its English form the word has undergone a gradual limitation of meaning. At first it seems to have denoted any clerk or registrar...


: , (. 19.); ë, .. , ¨ ( -1819) Oxford dictionary: actuary [aktri, -tj-] í a person who compiles and analyses statistics and uses them to calculate insurance risks and premiums... The current sense dates from the mid 19th cent. 1911 Encyclopödia Britannica: ACTUARY. ... then more particularly the secretary and adviser of any joint-stock company, but especially of an insurance company; and it is now applied specifically to one who makes those calculations as to the probabilities of human life, on which the practice of life assurance and the valuation of reversionary interests, deferred annuities, &c., are based. The first mention of the word in law is in the Friendly Societies Act of 1819, where it is used in the vague sense, "actuaries, or persons skilled in calculation," ...


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§.., ... . , 2014, 2. §Bulinskaya E., Gusak J., Muromskaya A. Discrete-time Insurance Model with Capital Injections and Reinsurance. Methodology and Computing in Applied Probability, 2014 §Shiryaev A., Burnaev E., Markov M., Panchekha A. Portfolio choice and cross-sectional skewness of hedge funds returns. Quantitative Finance, 2013. §.. . , 2013, 10 § .., .. . . . ., 2013, 58 §Ivanov R.V., Shiryaev A.N. On Duality Principle for Hedging Strategies in Diffusion Models. Theory of Probability and its Applications, 2012, 56, 3, p. 376-402 §... . , 2012, 4, 47-55. §Bulinskaya E., Yartseva D. Discrete time models with dividends and reinsurance. Proceedings of SMTDA 2010, Chania, Greece, June 8-11, 2010, p. 155-162 §Bulinskaya E., Gromov A. New approach to dynamic XL reinsurance. Proceedings of SMTDA 2010, Chania, Greece, June 8-11, 2010, p. 147-154 §Bulinskaya E.V. Stochastic Insurance Models:Their Optimality and Stability. Advances in Data Analysis. Theory and Applications, 2010, p. 129-140 § .. . . -, .15, 2010, 3, .37-43


§Patrick Boulongne, Daniel Pierre-Loti-Viaud, Vladimir Piterbarg. On average losses in the ruin problem with fractional Brownian motion as input. Extremes, 2009, 12, 1, 71-91. § .. . , 2009, 4, 1, . 85-92 § .. . í . 4. .1. ., 2009, .85-92. §Huesler J., Piterbarg V. A limit theorem for the time of ruin in a Gaussian ruin problem. Stochastic Processes and their Applications, 2008 , 118, 2014-2022. §Novikov A.A., Shiryaev A.N. On a stochastic version of the trading rule "buy and hold". Statistics and Risk Modeling, 2008, 26, 4, p. 289-302 §Eberlein E., Papapantoleon A., Shiryaev A.N. On the duality principle in option pricing: semimartingale setting. Finance and Stochastics, 2008, 2, p. 265-292 §Shiryaev A., Xu Z., Zhou X.Y. Thou shalt buy and hold. Quantitative Finance, 2008, 8 §Falin G. On the optimal pricing of a heterogeneous portfolio. ASTIN Bulletin, 2008, vol. 38, 1, p. 161-170 § . . , , .í , 2006, . 51, .3, 2006. . 465-475 § .. . . 1998, 5, 1, 134-140 § .. , . í , 1998, . 43, . 2, . 352- 357.


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..: Columbia University (May 2004), University South California (Los Angeles, USA, June 2005), Princeton University (November-December 2005),Halmstad University (Sweden, November-December 2006), Amsterdam University, (January 2007) .. Visiting Prof. ..: Heriot-Watt University (Edinburgh, UK) 2001 Visiting Lecturer

..: Kingston University (London, UK) 2009-2010 Professor of Actuarial Science and Mathematics


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§ §"Finance and Stochastics", §"Quantitative Finance" § () 1994-1998 §President of the Bachelier Finance Society 1998-1999

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§ § §ë ¨ 2005§Associate of The Society of Actuaries, USA (1995)



§International Conference "Kolmogorov and Contemporary Mathematics", June 16-21, 2003, Moscow §International Conference ë Stochastic Finance-2004 ¨, September 26-30, 2004, Lisbon, Portugal §International Conference "Finance and Control", April 2007, Portugal § " ", 100- .., 26-30 2012, § ë ¨, 24í28 2013, ,



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1. : í () 5 000 . ; í () 5 000 . . ( ) , i(4)= 8% . ) 7 511 . ) 7 813 . ) 8 984 . ) 9 353 . ) 9 828 . 2. . t=3,5. ) 1 = ln(1,06) , 200 . t=2; 500 . t=3 600 245 . ) 1 087 . ) 2 100 . ) 850 . ) 966 .

3. : 1) 100 . t=0; 200 . t=n 300 . t=2n. 2) 600 . t=10. i, . vn=0.76. ) 3.5 % ) 4.0 % ) 4.5 % ) 5.0 % ) 5.5 %


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5. 10 . ., , 12% . , 5 , , . ) 84 154 . ) 64 481 . ) 90 125 . ) 98 714 . ) 75 422 . 6. () 25 . 400 . , 15 i(12) 6% , 10 i(6) 6% . ) 41 414 . ) 43 123 . ) 44 356 . ) 45 809 . ) 46 703 .


7. 1 000 . . , . 15% . . ) 625 . . ) 756 . . ) 802 . . ) 712 . . ) 511 . . 8. C : (t)=0.05+0.002t. t=0 1 ., t = 7 . ) 1.290331 . ) 1.490331 . ) 1.390331 . ) 1.112901 . ) 1.248743 .


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11. x S = 10 000 . P=188 . - : i = 6% . : c = 3% . : D = 50 . : e = 3% . tV - t- . tV , , t+1V = 814.61 t- qx+t=0.0054. ) 684.46 ) 685.12 ) 691.97 ) 692.56 ) 697.23 . 16. 100002.2q[51]+0.5, . ) 91 ) 93 ) 95 ) 97 ) 99


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31. 10 000 , . , § p=0.03 , § , § . 400 50. , , 120 000, 1%. , , . ) 76.3% ) 89.8% ) 85.1% ) 88.2% ) 92.4% 33. . , : § =7 =2, § , §25% . , 15 000. ) 0.09 ) 0.11 ) 0.13 ) 0.15 ) 0.17


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1 2010 () () 9 . , 20 . : (Annals of Actuarial Science í ) (British Actuarial Journal í )



4 (stages ): 1. (Core technical í CT) 2. (Core applications í CA) 3. (Specialist Technical í ST)

4. (Specialist Applications í SA)



1. (Financial Mathematics í CT1) 2. (Finance and Financial Reporting í CT2) 3. (Probability and Mathematical Statistics í CT3) 4. (Models í CT4) 5. (Contingencies í CT5) 6. (Statistical Methods í CT6) 7. (Business Economics í CT7) 8. (Financial Economics í CT8) 9. (Business Awareness í CT9) : CT1-CT8 ã195, CT9 í ã1074.


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(Diploma in Actuarial Techniques): 9 (CT1-CT9). (Certificate in Finance and Investment): 6 (CT1, CT2, CT4, CT7, CT8, CT9) + (Actuarial Risk Management í CA1) . (Certificate in financial mathematics): " " ( CT1)


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-: 9 (CT1-CT9), 3 (CA1-CA3), ( ), . 400 . ã456 : - + 2 (ST) + 1 (SA) + ( ). 10 . . ã690 (Chartered Enterprise Risk Actuary í CERA): + ST9.


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1. . í 91 , 4%. í . , , . (3 ) 2. 8%. (i) . (1 ) (ii) . (1 ) (iii) . (2 ) ( 4 )


3. 1 2010 . ã120m ã140m 1 2011 . 1 2011 . ã200m. 1 2012 . ã600m. (i) , TWRR, . (3 ) (ii) , , MWRR, , TWRR. (2 ) ( 5 ) 4. 1 2012 , ã10. ã1 1 2012, 1 2013 1 2013. (i) , 8% , . (4 ) (ii) , . (2 ) ( 6 )


5. (i) . (4 ) (ii) (a) . (b) . 12 . 24% . , . (4 ) ( 8 )


6. i=6% 10 . . , . ã200, ã100. (i) . (2 ) (ii) (a) , . (b) , . (4 ) (iii) 15 . , 8% . . (3 ) ( 9 )


7. , ã200,000. 0.3 4% , 0.7 í 6%. 0.3 4% , 0.7 í 6%, . (i) , , , . (2 ) (ii) , , (i). ã200,000. (3 ) (iii) , , (i). (2 ) ( 7 )


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9. (i) , . (7 ) , , , . , 4% . (ii) , , 5%. (6 ) (iii) , 8% , 4% . (2 ) , , . 1: 79% , .


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10. . (i) , , . (3 ) P=ã3m. : A ã0.5m. ã0.55m. 10% , . , , , . B B ã0.64m . , . (ii) (a) B.


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CT5 í (Contingencies) 2012


1. (a) 4|5 q[60]1 (b) , AM92 [3 ] 2. P=ã3,000 . , , . , , : , ( ) , q=0.03, e=ã90 , i=4% ( ). . , , . [3 ]


(1 3. a50:15 IA)50:15 , AM92. [4 ]

4. , 60 55 , , ã100,000 . . : PMA92C20 , PFA92C20 ; 4% . . [4 ] 5. : (-40, -12, -6, -1, 5, -4, 8, 20, 25, 30). , , . : , [4 ]


6. (a) , [67;68] . AM92. (b) 0.5 q 67.25 , , (a). [4 ] 7. , . [6 ] 8. . [6 ] 9. (i) , . [2 ] (ii) ( (i)) , . [4 ] [ 6 ]


10. ( ã10,000) ( ã1,000). (a) , . (b) . [6 ] 11. (i) (crude mortality rate) (directly standardised mortality rate) . [4 ] : /: 50/100000, 55/95000, 60/80000. 1,250. (ii) ELT15 ( ) (standardised mortality ratio í SMR). [3 ] [ 7 ]


12. 10 ã100,000 ã50,000, 10 . . : 0.03 , 5%. [8 ]


13. x=20 n=20 . ( , ) SA=ã85,000 . , , n- SA (1 b)n1 , b=1.92308%, 40 SA (1 b) . P . : í AM92, í i=6% , 480% , 2.5% , ã325, ã75 . , , ã5 , . [10 ]


14. 40- 20 . ã200,000 , ã190,000 í .., .. ã10,000 ã10,000 () . . -; . (i) , - ã204. [4 ] , 10- 625 3 . (ii) 10- . [6 ] (iii) , (ii). [2 ] : í AM92, 4% , . [ 12 ]


15. 3 57 . ( ). ã150,000 . : 6% ( ), AM92, ã350, ã50, 15% , 2.5% , , , 6%. (i) , . [5 ] (ii) 0, ( ). [4 ] (iii) ( ). [6 ] (iv) - : (a) (iii). (b) 8%. [2 ][ 17 ]