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- らむ よどぎみ
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2 βdxβ r a, < E e uγ r ha d E e r dx e r γd e r βdx 3.2 a = {a} γ = {γ} max E e r dx e r γd e r βdx, 2 s.. dx = qand + σndz, 1 E e r uγ ha d, 3 a arg maxã E e r uγ hã d γ = {γ : γ, γ} a = {a : a, ā} W ; γ, a = E a e rs uγs has ds F. 5 5 F Y 1 dw ; γ, a = rw ; γ, a uγ + ha d + σny dz. 6 a 2 a arg maxã,ā Y qãn hã, <. 7 Y = h a q an = ya > ΠW ΠW = max E e rs 1 βqasn γs ds 8 s.. dw = rw uγ + ha d + σnyadz. 9 HJB rπw = max 1 βqan γ + rw uγ + ha Π W σ2 N 2 ya 2 Π W 1 a, γ 3 HJB 2 ΠW N 2. *1 1. *1 X γ 2. 2 qa = a, uγ = γ, ha =.5a 2 +.5a, N = 1, r =.1, β =.1, σ = 1 a b c 3.5 HJB 4 ISP CP ISP ISP 4.1 CP ISP 2, ISP C > δ ISP I C dc = I δcd. 11 gi, C := θi2 2C ISP ISPCP CP X ISP C *2 CP CP dx = pacd + σcdz. 12 Z = {Z, F; < } σ {F; < } {X; < } a CP pa a ISP CP CP ISP γc, γ CP γc *2 ISP C 2
3 uγc CP uγ 2 u = CP a hac ha γ ISP ISP λi, λ βc, β r CP a, < CP E e uγ r ha Cd ISP E e r dx e r γcd e r λid e r gi, Cd e r βcd CP ISP ISP CP I = δcp a = h a 4.2 ISP ISP CP a = {a} CP CP γ = {γ} max E e r pa γ β C λi gi, C d, 13 s.. dx = pacd + σcdz, 12 dc = I δcd, 11 E e r uγ ha Cd, 14 a arg max E e r uγ hã Cd. ã , < CP γ = {γ : γ, γ} I = {I : I, } CP a = {a : a, a} CP W ; γ, I, a = E a e rs uγs has Csds F. 16 CP 16 F Y W ; γ, I, a 1 dw ; γ, I, a = rw ; γ, I, a uγ ha C d+σy CdZ. 17 CP a 2 a arg max Y pã hã C, < 18 ã,a Y = h a p a = ya > CP W CP a ISP γ I ISP ΠW, C CP ISP ΠW, C = max E e rs pas γs β Cs λis γ,i,a gis, Cs ds 19 s.. dw = rw uγ ha C d + σyacdz, 2 dc = I δcd. 11 ISP 1 HJB r + δπw = max pa γ β + πw wπ w λ 2 2θ + r + δw uγ + ha π w σ2 ya 2 π w 21 ISP HJB aγ ISP 3 3 πw CP ISP 3 pa = a, uγ = γ, ha =.5a 2 +.4a, r =.11, δ =.4, θ = 2, β =.1, λ =.75, σ = 1 a CP ISP b c 4.4 CP ISP CP ISP ISP CP 5 SPFAP SPF AP AP N AP AP X dx = qa, µnd + σndz. 22 Z = {Z, F; < } σ {F; < } {X; < } a AP µ SPF qa, µ qa, µ a, µ qa,µ a = q a a, µ <, qa,µ µ = q µ a, µ < qa, µ, 1, a, µ, a, µ AP γ,, uγ uγ u < u = 3
4 AP a ha ha uγ h < AP a, < AP E e uγ r ha d r SPF βdxβ cµ cµ c < SPF E e r dx e r γd e r cµd βdx = E e 1 r βqa, µn γ cµ d. SPF ρ { E exp ρ e r } 1 βqa, µn γ cµ d , < AP γ = {γ : γ, γ} µ = {µ : µ, µ} AP a = {a : a, a} AP W ; γ, µ, a = E a e rs γs has ds F. 24 AP 24 F {Y } W ; γ, p, a 1 dw ; γ, µ, a = rw ; γ, µ, a uγ + ha d + σny dz. 25 a 2 a arg max qã, µy N hã, < 26 ã,a h Y = a q aa,µn = ya, µ > SPF 23 { JW = ρ 1 ln E exp ρ e rs 1 βqas, µsn } γs cµ ds SPF - ΠW = max JW = γ,µ,a ρ 1 ln ψw subjec o dw = rw ; γ, µ, a uγ + ha d + σnya, µdz. { ψw = max E exp ρ γ,p,a 29 e rs 1 βqas, µsn } γs cµ ds ΨW = ψw 1 { ΨW = max E exp ρ e rs 1 βqas, µsn γ,p,a γs cµ ds }. 31 HJB max rw uγ + ha Ψ W + 1 γ,µ,a 2 σ2 N 2 ya, µ 2 Ψ W ρ 1 βqa, µn γ cµ ΨW = HJB 32 HJB 32 γ µ a, W γ µ a SPF 3 ΠW ΨW ΠW ΨW ΠW 32 HJB rw uγ + ha Π W ρσ2 N 2 ya, µ 2 Π W 2 max γ,µ,a σ2 N 2 ya, µ 2 Π W + 1 βqa, µn γ cµ =. 33 SPF HJB 33 4 ΠW 4 qa, µ = a + µ, uγ = γ, ha =.5a 2 +.5a, cµ = 5µ 2, r =.1, β =.1, ρ =.5, σ = 1, N = 1 a SPF b c 5.4 SPF SPF SPF SPF ρ ΠW ρ Π W W AP SPF AP W AP Π ΠW 5.5 SPF AP AP - SPF SPF SPF 6 HJB 4
5 1 M. Armsrong: Compeion in Two-Sided Markes, Rand Journal of Economics, Vol.37, No.3, pp A. Hagiu: Two-Sided Plaform : Produc Variey and Pricing Srucures, Journal of Economics & Managemen Sraegy, Vol.18, No.4, pp J. Roche and J.Tirol: Plaform Compeion in Two-Sided Markes, Journal of Eurapean Economic Associaion, Vol.1, No.4, pp J. Roche and J. Tirol: Two-Sided Markes : a progress repor, Rand Journal of Economics, Vol.37, No.3, pp Y. Sannikov: A Coninuous Time Version of he Principal-Agen Problem, Review of Economic Journal Sudies, Vol.75, No.3, pp Masaru Unno and Hua Xu: Dynamic Opimal Revenue-Sharing Sraegy in E-Commerce, in A. König, A. Dengel, K. Hinkelmann, K. Kise, R.J. Howle, L.C. Jain eds. Knowledge-Based and Inelligen Informaion and Engineering Sysems, Par III, Lecure Noes in Arificial Inelligence, pp , Springer-Verlag, Berlin, Heidelberg ISP C Vol.131, No.4, pp
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Title 最適年金の理論 Author(s) 藤井, 隆雄 ; 林, 史明 ; 入谷, 純 ; 小黒, 一正 Citation Issue 2012-06 Date Type Technical Report Text Version publisher URL http://hdl.handle.net/10086/23085 Right Hitotsubashi University Repository
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