基于现金流优化的投资免赔契约

基于现金流优化的投资免赔契约

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1. ໓ᅣщݼ: 1001- 4098( 2011) 07-0076- 05 ࠎႿགྷࣁੀႪ߄֥๧ሧ૧ணఔჿX 宋庆凤 ( ฿ࣃն࿐ ༢๤۽ӱ࿹࣮෮, ฿ࣃ`300072) ᅋ`ေ: 从折现现金流最大化的角度研究了投资者的投资和免赔保险决策问题。在保险人赔付额限制条件 下, 建立了投资免赔契约模型, 给出了最优投资策略和最优免赔保险策略, 数值算例验证了模型的有效性。 ܱ࡯Ս: 免赔契约; 组合投资; 现金流; 猴群算法 ᇏ๭ٳোݼ: F840```໓ངѓ്઒: A 1　引言 ڄག๧ሧ֥ۚ؇҂ಒקྟथקਔ๧ሧᆀсྶҐ౼၂ ק֥Ҧ੻, ๙ݖކ৘֥ቆކٚൔ, ٳ೛ބ߄ࢳڄག, Ќᆣ ๧ሧࠃ׮֥ᆜุ൬ၭb၂Ϯط࿽, ๧ሧᆀѩ҂߶ࡼಆ҆ሧ ࣁ၂Ցྟ๧ೆ, ط൞ᄝ೏ۄ۱ᇛ௹ٳ஻๧ሧbᆌؓ؟௹๧ ሧ໙ี, Kung( 2008) ࡹ৫ਔቋն߄ቋᇔ൬ၭ֥؟௹ቆކ ๧ሧଆ྘[ 1] , Yan ֩( 2007) ࡹ৫ਔቋཬ߄ቋᇔ϶ٚҵ֥؟ ௹ቆކ๧ሧଆ྘[ 2] , ීࢱ֩( 2001) ࡹ৫ਔڄགӵ൳ି৯ჿ ඏ༯a ቋն߄ቋᇔ൬ၭ֥؟௹ቆކ๧ሧଆ྘[3] , Elt on ֩ ( 1974) , ჯफவ֩( 2003) ࿹࣮ਔ؟௹ཨٮ๧ሧ໙ี[ 4- 5] b ๧ሧᆀ૫ਢڄག, ູࡨഒ෥ാ, ॖၛܓઙЌགb ֒๧ሧ ᆀ๧ሧ൬ၭູڵൈ, Ќག܄ඳࡼοᅶఔჿܿקؓ๧ሧᆀ۳ ჍҀӊbCum mins( 1990) ॉ੮ਔЌགၹ෍, ᄎႨ׮෿ܿ߃ ٚم, ࡹ৫ਔ؟௹๧ሧЌགଆ྘[ 6] b૧ணఔჿܿקѓ֥໾ ෥ാᄝӑݖ૧ணحൈ, Ќགದڵᄳணӊӑݖ૧ணح֥҆ ٳ, ڎᄵ෥ാປಆႮ๧Ќದሱ࠭ӵք, ᄝЌᅰ๧Ќದնح ෥ാ֤֞Ҁӊ֥๝ൈཚ൳֮حЌٮ, ѩ౏ॖၛх૧Ќགದ ԩ৘նਈཬح෬ணσࡱطࢫസ৘ணٮႨ, ၹՎ൳֞๧Ќದ ބЌགದ֥ౝᩥbPaulsen( 1995) ࿹࣮ਔ๧ሧ૧ணଆ྘, ѩ ౏ٳ༅ਔܓઙЌགა๧ሧڄག֥ཌྷ޺ቔႨ[ 7] b ಖط, ၘႵ࿹࣮׻ࡼ๧ሧ൬ၭੱख़߂ູෛࠏэਈb൙ ൌഈ, ႮႿಌഒ৥ൎඔऌ, ࠇࠆ֤ཌྷܱྐ༏ླေڱԛۚح ٮႨ, ๧ሧᆀؓ๧ሧ০ੱa ๧ሧ෥ാ, മᇀ์གྷၹሰᆺି۳ ԛܙ࠹, ᆃᇕܙ࠹ջႵᇶܴྟ, ၹՎ, ࡼఃख़߂ູଆ޴эਈ ൞ކ৘֥[ 8] bЧ໓ࡼགྷࣁੀႪ߄৘ં[ 9] ႋႨ֞؟௹ቆކ๧ ሧथҦᇏ, ๝ൈॉ੮๧ሧᆀ֥๧Ќྛູ, Ֆ๧ሧᆀᅼགྷགྷ ࣁੀቋն߄֥࢘؇ԛؿ, ࡹ৫ଆ޴๧ሧ૧ணఔჿଆ྘b ؓႿགྷࣁੀႪ߄໙ี֥౰ࢳ, Russell( 1970) ࡹၰႋႨ ཌྟ߄ٚم[ 10] , ಖطཌྟ߄ေ౰่ࡱбࢠॎख़b൙ൌഈ, ࣪གྷࣁੀႪ߄໙ีޓ଴൐Ⴈཌྟ߄ٚم, ູՎ, Ч໓ᆌؓ ෮ࡹ৫֥ଆ޴૧ணఔჿଆ྘, ഡ࠹ࠎႿଆ޴ଆ୅֥ަಕෘ م( FSMA) ࣉྛ౰ࢳ, ඔᆴෘ২ඪૼෘم֥ॖྛྟބଆ྘ ֥Ⴕིྟb 2　投资免赔契约模型 ॉ੮๧ሧᆀ௹ԚႵ၂гሧࣁ, ေᄝ৵࿃֥ N ۱ᇛ௹ ࣉྛ๧ሧ, ௹ࡗ҂Ԏሧ, ҂ᇿሧb ๧ሧᆀᄝૄ၂௹׻૫ਢ๧ ሧ൬ၭੱູڵ֥ڄག, ູࡨഒ෥ാ, ླေܓઙ૧ணЌགb ࡌ ഡЌٮ൞૧ணح֥ݦඔ, ๧ЌದॖၛሱႮ࿊ᄴ૧ணحbਸ਼ ຓ, ๧ሧᆀؓ๧ሧ൬ၭੱa ๧ሧ෥ാa ์གྷၹሰᆺି۳ԛܙ ࠹, ᆃᇕܙ࠹ջႵᇶܴྟ, ၹՎࡼఃख़߂ູଆ޴эਈ[ 11] b 2. 1`ଆ྘ࡹ৫ ਷ ti ູਬൈख़ఏֻ֞ i ௹ൌགྷൈख़ᆸ֥ൈࡗӉ؇, Xki ູᄝֻ k ௹๧ሧӻ࿃ൈࡗ ti - tk ֥๧ሧح, rki ֻູ k ௹๧ ሧӻ࿃ൈࡗ ti - tk ൈ֥๧ሧ൬ၭੱ, r+ ki = max( rki , 0) , r- ki = - min( rki , 0) , ࠧ rki = r+ ki - r- ki , `k = 0, 1, l, i - 1; i = 1, 2, l, N ( 1) ᄵֻ i ௹֥෥ാح N i ູ N i = … i k= 0 Xki r- ki ( 2) ః౼ᆴٓຶ࠺ູ [ u, v ] b ਷ Di , I ( Di , N i ) ٳљֻູ i ௹֥૧ணحބணڱح, ૧ ணЌགܿקؿള൙ܣൈ, Ќགದؓ๧ЌҍӁ෥ാӑݖ૧ண ֻ29 जֻ7 ௹( ሹֻ211 ௹) 　　　　 　 　系　统　工　程 Vol. 29, No. 7 2011 ୍7 ᄅ````````` ` ` ` Systems Engineering July, 2011 X ൬۠ರ௹: 2011-01-18; ྩרರ௹: 2011-04-16 ቔᆀࡥࢺ: ස౩ڌ( 1983-) , ୯, ฿ࣃն࿐༢๤۽ӱ࿹࣮෮Ѱൖ࿹࣮ള, ࿹࣮ٚཟ: ҂ಒקྟथҦ, ᇆିෘمb
2. ح֥҆ٳڵᄳணӊ, ڎᄵ෥ാປಆႮ๧ሧᆀӵք, ၹՎ I ( Di , N i ) = max( Di , N i ) - Di ( 3) ``ഡЌགದؓ҂๝ᇛ௹ଖ๧ሧಕุ௜न෥ാ֥ܙ࠹ູ ౼ᆴٓຶ [ 0, L ] ֥ଆ޴эਈ, ࠺ູ N , ѩ۴ऌՎܙ࠹ᆴο ܄௜Ќٮჰᄵ൬౼Ќٮ, ࠧЌགఔჿડቀ Pi = E [ I ( Di , N ) ] , `i = 1, 2, l, N ( 4) ``๧ሧᆀ๧ሧބ๧Ќ֥थҦ໙ีູ: ಒקЌག܄ඳ҂঄ Ч֥ჿඏ่ࡱ༯, ֻk ௹๧ሧ౏ӻ࿃ൈࡗູ ti - tk ֥๧ሧ ح Xki ބૄ௹֥૧ணح Di , ၛ൐ሱ֥࠭ᅼགྷགྷࣁቋն߄b ਷ W i ູ๧ሧᆀֻ i ௹֥གྷࣁ, r ູᅼགྷၹሰ, ᄵࠎႿགྷࣁ ੀႪ߄֥๧ሧ૧ணఔჿଆ྘ູ max X ki , D i E … N i= 1 W i exp( - rti ) s. t . `Wi+ 1 = Wi - … N j = i+ 1 Xij - P i + … i k= 0 Xki ( 1 + rki ) `````` + I( Di , N i ) ```Pi œ %[ I( Di , N i ) ] ```Wi - … N j = i+ 1 Xij - P i œ 0 ```k = 0, 1, l, i - 1 ```i = 1, 2, l, N ( 5) ఃᇏ, ֻ၂۱ჿඏູ۲௹གྷࣁᆴડቀ่ࡱ, Ⴗ؊ֻؽཛі ൕᄝֻ i ௹๧ሧ֞ᆭު N - i ௹֥ሹح, ֻ೘ཛіൕֻ i ௹֥Ќٮ, ֻඹཛіൕ෮Ⴕֻ֞ i + 1 ௹౼གྷ֥Ч০ބ, ֻ ໴ཛіൕֻ i ௹ணڱح, ֻؽ۱ჿඏູ۲௹Ќག܄ඳ൬౼ Ќٮ҂ཬႿ௹ຬணڱح, ֻ೘۱ჿඏູ۲௹གྷࣁᆴ٤ڵb 2. 2`ଆ྘ٳ༅ ଆ྘( 5) ട֥ࠣଆ޴эਈࢠ؟, ౏҂ປಆ൞थҦэਈ Xki , Di ֥ཁൔіղྙൔ, ູՎ۳ԛଆ྘( 5) ֥֩ࡎଆ྘b ק৘1`ҐႨЌٮჰᄵ( 4) קࡎൈ, ଆ྘( 5) ֩ࡎႿ max X ki , D i E … N i= 1 Wi exp( - rti ) s. t. `Wi+ 1 = W i - … N j = i+ 1 Xij - ‘ L Di # ( x ) dx `````` + … i k= 0 Xki ( 1 + r+ ki ) - min Di , … i k= 0 Xki r- ki ``` ‘ L Di # ( x) dx œ‘ v Di # i ( x) dx ```Wi - … N j = i+ 1 Xij - ‘ L Di # ( x) d x œ 0 ```k = 0, 1, l, i - 1 ```i = 1, 2, l, N ( 6) ఃᇏ, U i ( x ) a 5 i ( x) ٳљູ( 2) ᇏ N i ֥ॖྐྟૡ؇ބٳ҃ ݦඔ, U ( x ) a 5 ( x ) ٳљູ( 4) ᇏ N֥ॖྐྟૡ؇ބٳ҃ݦ ඔ, # i ( x) = 1 - 5 i ( x ) , # ( x ) = 1 - 5 ( x) b ᆣૼ` ਷ G = max( Di , N ) , ᄵ ` Cr{G › x} = Cr{m ax( Di , N ) › x } = Cr{ {Di › x } ˆ {N› x }} = Cr{Di › x} ƒ Cr{N› x} ( 7) Cr{ Di › x} = 0, `x < Di 1, `x œ Di ֤ࠧ Cr{ G› x } = 0, Cr{ N› x }, ` x < Di x œ Di ෮ၛЌٮ( 4) ູ ` P i = E[ I ( Di , N ) ] = E[ max( Di , N ) ] - Di = ‘ +  -  xd Cr{ G› x } - Di = ‘ L 0 xdCr{ G› x} - Di = lim E ¹0 ‘ D i - E 0 xdCr{G › x} + lim E ¹0 ‘ D i Di- E xdCr{ G› x} ` + ‘ L Di xdCr{G › x} - Di = Di Cr{ N› Di } + ‘ L Di xdCr{N› x} - Di = Di 5 ( Di ) + ‘ L Di x U ( x ) dx - Di = Di 5 ( Di ) + x5 ( x) ûL Di - ‘ L D i 5 ( x) dx - Di = Di 5 ( Di ) + L - Di 5 ( Di ) - ‘ L Di [ 1 - # ( x) ] dx - Di = ‘ L Di # ( x) dx ( 8) ๝৘, ணڱح( 3) ֥௹ຬᆴູ E[ I( Di , N i ) ] = ‘ v Di # i ( x ) dx ( 9) Ⴎ( 3) ᆩ I ( Di , N i ) = N i - min( Di , N i ) ( 10) ෮ၛ۲௹གྷࣁᆴ ` Wi+ 1 = W i - … N j = i+ 1 Xij - Pi + … i k= 0 Xki ( 1 + r+ ki ) - N i + I( Di , N i ) = W i - … N j = i+ 1 Xij - ‘ L Di # ( x ) dx + … i k= 0 Xki ( 1 + r+ ki ) ` - min Di , … i k= 0 Xki r- ki ( 11) 77 ֻ7 ௹` ` ``````````ස౩ڌ: ࠎႿགྷࣁੀႪ߄֥๧ሧ૧ணఔჿ
3. ק৘1 ֤ᆣb ଆ྘( 6) ෙಖ൞थҦэਈ Xki , Di ֥ཁൔіղൔ, ֌උ Ⴟ၂োگᄖ֥ଆ޴٤ཌྟܿ߃໙ี, ໭مႨԮ๤ٚمႵི ౰ࢳbູՎ, ༯ࢫࡼഡ࠹౰ࢳھଆ྘֥၂۱ࠎႿଆ޴ଆ୅ ֥ަಕෘم( FSMA) b 3　基于模糊模拟的猴群算法 ަಕෘم( MA) [12] ൞ଆ୅ަሰ஁೶ݖӱطഡ࠹֥ಕ Ⴊ߄ෘم, ০Ⴈଢѓݦඔᄝ֒భࢳ֥ເะ؇ྐ༏, ๙ݖަ ಕᇏૄᆺަሰ஁a ຬa ๋೘۱׮ቔݖӱ, ҂؎ෆ෬ࢳॢࡗ֥ ۲۱౵თbෘمЧദླေטᆜ֥ҕඔࢠഒ; ౏ᇕಕܿଆؓ ໙ีົඔ҂ૹۋ, ෮ၛॖၛॹ෎Ⴕི֥౰ࢳۚົඔa ؟ࠞ ᆴ໙ี֥ಆअቋႪࢳb ౰ࢳଆ޴эਈ… N i= 1 W i exp( - rti ) ௹ຬᆴ֥ଆ޴ଆ୅ ( FS) ෘم: ҄ᇧ1: ਷e = 0; 7 ( W) = … N i= 1 Wi exp( - rti ) , ఃᇏ W = ( W1 , W2 , l, WN ) T . ҄ᇧ2: नᄋӁള H j k ( j = 1, 2, l, M ; k = 1, 2, l, K ) ൐֤ P os( H j k ) œ E, ఃᇏ M ൞ଆ྘֥थҦэਈඔ, K ൞၂ ۱ԉٳն֥ඔ, E൞၂۱ԉٳཬ֥ඔb ҄ᇧ 3: ਷ H k = ( H 1k , H 2k , l, H Mk ) , vk = P os( H 1k ) ƒ Pos( H 2k ) ƒ l ƒ Pos( H Mk ) , a = 7 ( W( H 1 ) ) ƒ 7 ( W ( H 2 ) ) ƒ lƒ 7 ( W ( H k ) ) , b = 7 ( W ( H 1 ) ) „7 ( W ( H 2 ) ) „ l „ 7 ( W( H k ) ) b ҄ ᇧ 4: ਷ L = ( max k {v k û7 ( W ( H k ) ) œ r} + min k { vk û7 ( W ( H k ) ) < r}) / 2, ఃᇏr ൞ [ a, b] ᇏෛࠏඔ; ೏ r œ0, ᄵ਷ e = e + L , ڎᄵe = e - L , ᇗگՎ҄ᇧ K Ցb ҄ᇧ 5: ൻԛ E [ 7 ( W ) ] = a „ 0 + b ƒ 0 + e( b - a) / K . ަಕෘم[ 12] ஁ݖӱႨটෆ෬अ҆ቋႪࢳ, ຬݖӱႨ ট࿙ᅳб֒భቋႪࢳ۷Ⴊ֥ࢳ, ๋ݖӱॖၛॹ෎֥֞ః෰ ෆ෬౵თ, ၛٝཊೆअ҆ቋႪb ਷ f : R( N2+ 3N) / 2 ¹ R ູ f ( x ) = E … N i= 1 Wi exp( - rti ) ( 12) ఃᇏ, x T = ( X01 , X02 , l, X0N , X12 , X13 , l, X1N , l, X(N - 1)N , D1 , l, D N ) ‰ R( N2+ 3N )/ 2. ౰ࢳଆ྘( 6) ֥ࠎႿଆ޴ଆ୅֥ަಕෘم( FSMA) і ඍೂ༯: ҄ᇧ 1: ҕඔഡק: थҦэਈ۱ඔ M, ଆ޴ଆ୅Ցඔ K , ަಕܿଆ P , ஁֥Ցඔ Nc , ஁֥҄Ӊ a, ൪့Ӊ؇ b, ๋֥౵ࡗ [ c, d] , םսՑඔ S . ҄ᇧ2: Ԛ൓ׄളӮ: ႮॖྛთෛࠏളӮԚ൓໊ᇂ xij , i = 1, 2, l, P ; j = 1, 2, l, M. ҄ᇧ3: ஁: ࠹ෘଢѓݦඔ( 12) ֒భׄ xi ເะ؇ ¶f ij ( xi ) = f ( xi + ¶xi ) - f ( xi - ¶xi ) 2¶x ij ( 13) ఃᇏ, ¶x ij ડቀ Pr( {¶xij = a}) = Pr( { ¶x ij = - a} ) = 0. 5, ଢѓݦඔ( 12) ֥ᆴႮభ૫֥ଆ޴ଆ୅( FS) ෘم ౰֤b೏ xij + sign( ¶f ij ( xi ) ) ॖ ྛ, ਷ xij = xij + sign( ¶f ij ( x i ) ) b ᇗگՎ҄ᇧ Nc Ցb ҄ᇧ4: ຬ: Ⴎ ( xij - b, x ij + b) ෛࠏളӁׄx £ i , ০Ⴈ ଆ޴ଆ୅࠹ෘଢѓݦඔ f ( x £ i ) b೏ x£ i ᄝॖྛთଽ, ౏ f ( x £ i ) > f ( xi ) , ᄵ਷ xi = x£ i . ᇗگՎ҄ᇧ Nc Ցb ҄ᇧ5: ๋: Ⴎ [ c, d] ෛࠏളӁඔ S , ೏xi + S( pj - x i ) ᄝॖྛ თଽ, ᄵ਷ x i = xi + S( p j - xi ) , ఃᇏ p j = … P i= 1 xij / P. ҄ᇧ6: ᇗگ҄ᇧ3a ҄ᇧ4a ҄ᇧ5 ܋ S ՑbൻԛቋႪ ଢѓݦඔ f ( x* ) ބቋႪࢳ x * . 4　数值算例与分析 4. 1`ඔᆴෘ২ ଖ๧ሧᆀؓԚ൓ሧӁ100 ຣჭᄝ3 ୍ଽ܋ٳ3 ۱ᇛ௹ ࣉྛ๧ሧ, ఃᇏ ti = i, i = 1, 2, 3bၛݓ࿹ຩࣁವඔऌ ९ҍӁЌགٳ܄ඳ2006j2009 ୍ြༀ๤࠹іູ၇ऌ, ࠹ ෘ၂aؽa೘୍௹௜न൬ၭੱູᆞ෿ٳ֥҃ෛࠏэਈ, ࡮ і1b і1`ֻ k ௹֞ i ௹০ੱ֥नᆴაѓሙҵ( % ) ( uk1 , Rk1 ) ( uk2 , Rk2 ) ( uk3 , Rk3 ) ( u0i , R0i ) ( 4. 2, 5) ( 7. 8, 9) ( 11, 14) ( u1i , R1i ) ( 6. 5, 7) ( 9. 6, 11) ( u2i , R2i ) ( 5. 4, 8) ၹЌགದ҂ିࣚಒ۳ԛഠ߶௜न෥ാੱ, ๧ሧᆀၧ҂ ିࣚಒ۳ԛ์གྷၹሰބ๧ሧ൬ၭੱ, ۴ऌ۲ᇕၹ෍֤ყ௹ ഠ߶௜न෥ാੱູ೘࢘ଆ޴эਈ N= ( 0, 0. 05, 0. 12) , ყ ௹์གྷੱູ೘࢘ଆ޴эਈr = ( 0. 02, 0. 03, 0. 04) , ყ௹๧ ሧ൬ၭੱູ೘࢘ଆ޴эਈೂі2 ෮ൕb і2`ֻ k ௹֞ i ௹০ੱܙ࠹ᆴ rki ( % ) rk1 rk2 rk3 r0i ( - 1. 5, 5, 10) ( - 2, 7, 15) ( - 4. 6, 12, 20) r1i ( - 2, 6, 11) ( - 3, 9, 16) r2i ( - 3, 6. 4, 12) 78 ༢`๤`۽`ӱ``````````````````2011 ୍
4. ``Ⴎൔ( 2) ֤۲௹෥ാູ೘࢘ଆ޴эਈ: N 1 = ( 0, 0, 0. 01X01 ) , N 2 = ( 0, 0, 0. 02X02 + 0. 02X12 ) , N 3 = ( 0, 0, 0. 05X03 + 0. 03X13 + 0. 03X23 ) b 4. 2`ҕඔഡᇂ ҐႨࠎႿଆ޴ଆ୅֥ަಕෘمؓଆ྘( 6) ࣉྛ౰ࢳ, ۴ऌႪ߄ଆ྘ࠣഈඍऎุ໙ี, ҩ൫ު, ቋࡄҕඔഡᇂູ: थҦэਈ۱ඔ M = ( 32 + 3 €3) / 2= 9, ަಕܿଆP = 5, ଆ޴ଆ୅Ցඔ K = 1000, ஁Ցඔ N c = 2000, ๋౵ࡗ[ c, d] = [ 0, 100] , םսՑඔ S = 60, ෘمႨC+ + щӱൌགྷ, ӱ ྽ᄎྛߌ࣢ູ۱ದPCb 4. 3`࠹ෘࢲݔ ഈඍෘ২ႨFSM A ᄎྛ౰ࢳ, ০ੱູෛࠏэਈൈ۲௹ ቋႪ๧ሧحೂі 3 ෮ൕ, ቋնགྷࣁᆴ116. 8032 ຣb ҕඔູଆ޴эਈൈ۲௹ቋႪ๧ሧحೂі4 ෮ൕ, ቋႪ Ќག ( Di , P i ) ( i = 1, 2, 3) ٳљູ( 0, 0) , ( 1. 2, 0. 22) , ( 2. 6, 0. 18) , ቋնགྷࣁᆴ117. 9606 ຣჭb ҕඔູଆ޴эਈ֌໭Ќགൈ, ۲௹ቋႪ๧ሧحೂі5 ෮ൕ, ቋնགྷࣁᆴູ109. 5775 ຣჭb ೏҂ॉ੮ሧࣁ֥ൈࡗࡎᆴ, ࠧᄝഈඍଆ྘ᇏ҂࠺ሧࣁ ֥ൈࡗࡎᆴ, ଢѓݦඔ๼߄ູ max X ki , D i E … N i= 1 W i , ჿඏ҂э, Վൈ۲௹ቋႪ๧ሧحೂі 6 ෮ൕ, ቋႪЌག( Di , P i ) ٳљ ູ( 0, 0) , ( 1. 13, 0. 213) , ( 2. 52, 0. 176) , ቋնགྷࣁᆴູ 115. 8713 ຣჭb і3`ઙЌགෛࠏ౦ྙ༯۲௹๧ሧح Xki ( ຣჭ) Xk1 Xk2 Xk3 X0i 22. 8935 38. 7953 32. 6910 X1i 38. 6532 37. 8024 X2i 39. 5145 і4`ઙЌགଆ޴౦ྙ༯۲௹๧ሧح Xki ( ຣჭ) Xk1 Xk2 Xk3 X0i 23. 3962 39. 0129 33. 2119 X1i 38. 8905 37. 9683 X2i 40. 0501 і5`໭Ќགଆ޴౦ྙ༯۲௹๧ሧح Xki ( ຣჭ) Xk1 Xk2 Xk3 X0i 21. 5937 37. 4996 31. 2955 X1i 37. 8570 36. 8040 X2i 38. 5141 і 6`҂ॉ੮ሧࣁൈࡗࡎᆴൈ۲௹๧ሧح Xki ( ຣჭ) Xk1 Xk2 Xk3 X0i 22. 7143 38. 7689 32. 2245 X1i 37. 7457 36. 8624 X2i 38. 8836 4. 4`ࢲݔٳ༅ Ⴎі3a і 4 ॖၛुԛ, ܓઙЌགభิ༯, ቋնགྷࣁᆴ ᄝҕඔູଆ޴эਈൈбҕඔູෛࠏэਈൈิۚਔ1. 1574 ຣჭb Ֆі4a і5 ॖၛुԛ, ҕඔູଆ޴эਈభิ༯, ቋն གྷࣁᆴᄝܓઙЌགൈбીႵЌགൈิۚਔ 8. 3831 ຣჭb Ⴎі 4a і 6 ॖၛुԛ, ܓઙЌག౏ҕඔູଆ޴эਈభิ ༯, ቋնགྷࣁᆴᄝॉ੮ൈࡗࡎᆴൈбીႵॉ੮ൈࡗࡎᆴൈ ิۚ2. 0893 ຣჭb ሸഈ, ॖၛ֤֞ೂ༯ࢲં: ¹ Ⴎі3a і4 ॖၛुԛ, ଆ޴эਈࢠݺֹّ႘ਔЌག ದބ๧ሧᆀ֥ᇶܴ჻ຬ, ൡ֥֒ܙ࠹෥ാੱބ๧ሧ൬ၭ ੱ֥ᆴ, ൐๧Ќٳ༅ބ๧ሧٳ༅۷ऎ಼ྟ, Ֆطॖ֤֞ડ ၩ֥Ќགఔჿބ๧ሧҦ੻b º Ⴎі4a і5 ᆩ, ܓઙЌག൐֤གྷࣁᆴႵ෮ิۚ, ၂ קӱ؇ഈॖၛٳ೛ѩࢆ֮ڄགb » Ⴎі 4a і 6 ᆩ, གྷࣁੀႪ߄ॉ੮ਔሧࣁ֥ൈࡗࡎ ᆴ, ؓ؟ᇛ௹๧ሧႪ߄ऎႵࢠն֥ࡎᆴb 5　结论 ၛສؓ؟ᇛ௹๧ሧ֥࿹࣮, अཋႿᄝෛࠏߌ࣢༯ቋն ߄๧ሧᆀ֥௹ຬིႨ, ط҂ॉ੮ሧࣁ֥ൈࡗࡎᆴࠇ๧Ќࠃ ׮ؓ๧ሧ֥႕ཙbЧ໓۴ऌ؟௹๧ሧࠃ׮֥หׄ, ႋႨགྷ ࣁੀႪ߄৘ં, ๝ൈॉ੮๧ሧ൬ၭੱބ෥ാ֥҂ಒקྟ, ࡼ๧ሧࠃ׮ބ๧Ќࠃ׮ࢲކఏট࿹࣮, ܒࡹਔଆ޴๧ሧ૧ ணఔჿଆ྘, ѩҐႨࠎႿଆ޴ଆ୅֥ަಕෘمࣉྛ౰ࢳ, ࢲݔіૼ, ଆ޴эਈॖၛࢠݺֹّ႘थҦᆀ֥ᇶܴ჻ຬ, གྷࣁੀႪ߄ᄝ๧ሧथҦᇏఏ֞ਔᇗေቔႨ, طܓઙЌག ิۚਔ࣪གྷࣁᆴ, ᆃؓႿ๧ሧᆀࠣࣁವࠏܒ֥ЌᆴᄹᆴႵ ࠒ֥ࠞ৘ંބགྷൌၩၬb ҕॉ໓ང: [ 1] `Kung J. Mult i- period asset allocation by stochastic dynamic programming [ J ] . Applied M athematics and Comput ation, 2008, 199( 1) : 341j348. [ 2] `Yan W, et al. Mult i- period semi- variance portfolio selection: M odel and numerical solution [ J ] . Applied Mathematics and Computat ion, 2007, 194 ( 1) : 128j134. 79 ֻ7 ௹` ` ``````````ස౩ڌ: ࠎႿགྷࣁੀႪ߄֥๧ሧ૧ணఔჿ
5. [ 3] `ීࢱ, ਾࡅሐ. ؟ᇛ௹ሧӁ๧ሧ֥׮෿ܿ߃थҦଆ྘ [ J] . ᇏݓܵ৘॓࿐, 2001, 9( 3) : 55j60. [ 4] `Elton E, Gruber M. The multi period consumption investment problem and single period analysis [ J] . Oxford Economic Papers, 1974, 26( 2) : 289j301. [ 5] `ჯफவ, ීࢱ. ۱ದཨٮ๧ሧ؟ᇛ௹थҦଆ྘[ J] . ᇏ ݓܵ৘॓࿐, 2003, 11( 5) : 12j15. [ 6] `Cummins J. M ulti- period discounted cash flow rate m aking models in property- liability insurance[ J ] . Journal of Risk and Insurance, 1990, 57 ( 1) : 79 j 109. [ 7] ` Paulsen J. Optimal per claim deductibility in in- surance with t he possibilit y of risky invest ment s [ J] . Insurance: Mat hematics and Economics, 1995, 17( 2) : 133j147. [ 8] `ӧݓ޿, ӧ൬, ລ൰ဝ. ౵ࡗඔଆ޴๧ሧቆކଆ྘ [ J] . ༢๤۽ӱ, 2007, 25( 8) : 34j37. [ 9] `Erenguc S, T ufekci S , Zappe C. Solving time/ cost trade- off problems with discounted cash flows using generalized benders decomposition [ J ] . Naval Research Logist ics, 1993, 40( 1) : 25j50. [ 10] `Russell A. Cash flow s in networks [ J ] . Manage- ment Science, 1970, 16( 5) : 357j73. [ 11] `Liu B, Liu Y. Expected value of fuzzy variable and fuzzy expected value models [ J ] . IEEE Transaction on Fuzzy Syst ems, 2002, 10( 4) : 445j 450. [ 12] `Zhao R, T ang W. Monkey algorithm for global numerical optim ization [ J] . Journal of U ncertain Systems, 2008, 2( 3) : 165j176. Deductible Contract to Investment Based on Cash Flow Optimization SONG Qing-feng ( Institute of Systems Engineering, Tianjin University, T ianjin 300072, China) Abstract: T his paper explores investorns decision on invest ment and deduct ible insurance, from the insured n s perspect ive of maximizat ion the discounted cash flow . A deductible contract model w it h invest ment and t he constraint of limited compensation is built , and the optimal invest ment strategies and the optimal deductible insurance are obt ained. A numerical example is presented, w hich illustrates the effect iveness of the proposed model. Key words: Deductible Contract; Portfolio Investment; Cash Flow ; Monkey Algorithm 80 ༢`๤`۽`ӱ``````````````````2011 ୍