PFI

Size: px

Start display at page:

Download "PFI"

れいなたけくま
5 years ago
Views:

1 PFI

2 PFI PFI

3 A 1 6

4 1 PFI Private Finance Initiative 10 PFI PFI PFI SPC 14) PFI SPC PFI 2 1

6 2 2.1 PFI PFI 14) PFI PFI 12) PFI 13) PFI PFI 11) PFI PFI principal-agent PA PA PA PA 3

7 2.2 PFI 11) PFI PFI 12) NPV t 4

8 Green 7) Diamond 5) Green Spear Srivastava 7) Thomas Worrall 10) Gromb 8) DeMarzo Fishman 6) Gromb 8) Biais 1) Demarzo DeMarzo Fishman 3) 5

9 6

10 3 3.1 PFI PFI I t d t t Y t {Y t } s < t E s [Y t ] = E [Y t ] = µ t r γ r Y 0 t Y t t s t Y t s t d t Y t s t Y t + s t d t (> 0) 1 λ [0, 1] 1 λ λ = 0 λ > 0 t Y t 7

11 t t W t t W t R t 0 L t s < t W s e r(t s) W t (3.1) R s e γ(t s) R t (3.2) L s e γ(t s) L t (3.3) (3.1) (3.2) (3.3) s Vs F B max e r(t s) Y t + e r(τ s) ( W τ + R τ + L τ ) (3.4) τ s s<t τ T V t W t + R t + L t for t T (3.5) t = T T 0 T T T T -3.1 t d t 8

12 第期第期キャッシュフローが実現されるエージェントがを政府に報告する政府が補助金報酬を支払うエージェントあるいは政府が事業を中止 3.1 t s t t h t x t (h t ) h t t Y t t λ(y t +s t d t )+x t (h t ) h t t p t (h t ) 3.2 h t x t p t σ = (x, p) φ φ t s t [0, d t Y 0 t ] σ σ revelation principle 9) σ φ [ ] A t (σ, φ) = E t<s τ e γ(s t) (λ (Y s + s s d s ) + x s ) + e γ(τ t) R τ σ, φ, τ > t φ σ A t (σ, φ) (σ, φ) incentive compatible 9

13 σ φ t [ ] B t (σ, φ) = E t<s τ e r(s t) ( s s x s )) e r(τ t) W τ σ, φ, τ > t (σ, φ) A t B t common knowledge t a a subject to b e t(a) max σ,φ B t (σ, φ) A t (σ, φ) = a = max A t (σ, φ ) (3.6) φ (3.6) b e t t be t a a b e t (a) = b e t (a) t a t a a t -3.1 t Y t t t + 1 b e t t t b d t by t bd t b y t Y t T (σ, φ) 3 10

14 3.2.1 T T + T b e T T a > 0 γ r T + e γ(t + T ) a b e e (γ r)(t + T ) a T (a) = a 0 a < 0 (3.7) T r a a < 0 T T (3.7) t(< T ) b e t t -3.1 b e t 1 bd t bd t 2 b y t by t t b e t b e T a 0 b e t a e t t x t b d t b d t ad t R t a d t a d t ( W t, R t ) b e t (a) convex hull ( W t, R t ) b e t(a) -3.2 ( W t, R t ) b e t be t a L t l t a d t [R t, a L t ] 11

15 配当区間エージェントの利得継続区間清算区間政府の利得 3.2 b e t bd t p t (a d t ) = al t a d t a L t R t (3.8) a L t p t h t a d t p t a d t x t b e t a1 t x t (a d t ) = max(a d t a 1 t, 0) (3.9) 12

16 b d t b d t bd t (a) 1 (3.10) T a L T = γ > r a 1 T = R T P T = 1, x T = a d T R T, b d T (ad T ) = W T (a d T R T ) b d t 1 b e t l t > 1 l t = sup{ be t(a) + W t a R t : a > R t } a L t = inf{a > R t : b e t l t }, a 1 t = inf{a : b e t 1} b d t (a d t ) = b e t(a 1 t ) (a d t a 1 t ) a d t a 1 t b e t(a d t ) a L t a d t a 1 t b e t(a L t ) l t (a L t a d t ) R t at d < a L t a d t < R t (3.11) l t 1 a L t =, a 1 t = R t b d t (a d W t (a d t R t ) t ) = a d t R t a d t < R t (3.12) b d t (3.10) b d t by t t t Y t s t s t a d t a d t 13

17 s t = d t Y t b y t (ay t ) = max a d t ( ) E[Y t + b d t (a d t (Y t ))] (3.13) s.t.(ic) a d t (Y t ) a d t (y) + λ(y t y) y [Y 0 t, Y t ] (3.14) E[a d t (Y t )] = a y t (3.15) a d t t a y t E[a d t (Y t )] (3.13) (3.14) a d t (y) λy y a d t (y) y 3.14 ŷ t (Y t ) Y t a d t (ŷ t ) a d t (Yt ) = a d t (ŷ t (Y t )) + λ(y t ŷ t (Y t )) 3.14 a d t (ŷ t (Y t )) + λ(y t ŷ t (Y t )) a d t (Y t ) for y [Y 0 t, Y t ] a d t (Y t ) a d t (Yt ) = a d t (Y t ) ŷ t (Y t ) Y t ŷ t Y t [Y t + b d t (a d t (Yt ))] [ŷ t + b d t (a d t (ŷ t ))] = Y t ŷ t + b d t (a d t (ŷ t ) + λ(y t ŷ t )) b d t (a d t (ŷ t )) b d b t (a) 1 d t (ad t (ŷ t)+λ(y t ŷ t )) b d t (ad t (ŷ t)) a d t (ŷ t)+λ(y t ŷ t ) a d t (ŷ 1 t) [Y t + b d t (a d t (Yt ))] [ŷ t + b d t (a d t (ŷ t ))] Y t ŷ t λ(y t ŷ t ) = (Y t ŷ t )(1 λ) 0 14

18 2 b d t (3.10) µ t E[Y t ] y a d t (y) = a y t + λ(y µ t) (3.16) [ ] b y t (ay t ) = µ t + E b d t (a y t + λ(y t µ t )) (3.17) b y t 2 2 γ > r 1 (3.9) (3.16) 2 x t = λ max(y t D t, 0) (3.18) D t = µ t + λ 1 (a 1 t a y t ) b y t be t 1 2 t a t a γ r 15

19 プロジェクト期間キャッシュフロー補償及び終了決定 b y t t b e t (a e t ) = e r(t t ) b y t (eγ(t t ) a e t ) (3.19) b e t (3.7) T b e T T -3.3 s t s = t a e s t a y t = eγ(t s) a e s Y t a d t ad t x t p t a e t R t at d a L t 0 a d t = x t + a e t ad t < a L t p t x t = 0 a d t = (1 p t )a e t + p t R t

20 I Y 0 a d 0 = arg max b d 0(a) (3.20) a R 0 +Y 0 Y 0 + b d 0 (ad 0 ) I ad 0 al 0 1 a d 0 a

21 4 4.1 T k t f T ˆr t 0 c L t t z > 0 N t z p t (z) = z/n t 1 p t (z) p t (z) 100 z (1 p t (z)) 1 p t (z) 100 L t W t p t p t Y 0 I Y t 18

22 プロジェクト外部経済便益政府クレジットライン引出返済エージェント投資家配当株主 4.1 Y t s t d t λ 100 (1 λ) 100 T = min{t : l t 1} T t I Y 0 d t = (1 + r 1 )(1 (1 + r) T ) L T t k t d t k t k t k t = µ t + λ 1 [ a 1 t e γ(t t ) a 1 t ], t (0, T ] (4.1) t s t = d t k t ˆr = γ c L t = λ 1 ( a 1 t a L ) t, t [0, T ) (4.2) 19

23 N t = λ 1 ( a L ) t R t, t [0, T ) (4.3) 0 c d 0 = ( λ 1 a 1 0 ) al 0 a d 0 (3.20) T c L T = 0 N T = L T T c d t a d t = a 1 t λc d t (4.4) 0 a 1 t 0 (4.2) a 1 t λc L t = a 1 t λ(λ 1 (a 1 t a L t )) = a L t 3 Y 3 1 Y 2 Y 3 Y (1 λ) 1 λ 2 λ 100 λ λ 3 (4.4) (4.4) 1 λ 3 λ 20

24 3 1 λ 3) 2) 1 k t t 0 k t µ t (4.4) a 1 t λ(k t µ t ) a 1 t a 1 t = e γ(t t ) [ a 1 t λ(k t µ t ) ] (4.5) (4.5) k t (4.1) 4 k t s t 4 21

25 5 1 PFI PFI 2 PFI

26 4 23

27 A 1 b d t -3.2 ( W t, R t ) R t R t a < R t b d t (a) = R t ( W t, R t ) b e t l t l t > 1 b e t al t a d t [R t, a L t ] a L t p t (??) p t R t + (1 p t )a L t = a d t p t ( W t ) + (1 p t )b e t (a L t ) = b e t (a L t ) + al t a d t a L t R (L t b e t(a L t )) = b e t (a L t ) l t (a L t R t ) t l t > 1 a 1 t a L t a1 t [R t, a 1 t ] a 1 t (3.18) x t b d t (a d t ) = b e t (a 1 t ) d t = b e t(a 1 t ) (a d t a 1 t ) l t 1 1 b d t (a d t ) = L t d t = L t (a d t R t ), for a d R t = a 1 t 2 (3.13) ŷ t (Y t ) Y t a d t (ŷ t ) a d t (Yt ) = a d t (ŷ t (Y t )) + λ(y t ŷ t (Y t )) (3.14) a d t (ŷ t (Y t )) + λ(y t ŷ t (Y t )) a d t (Y t ) for y [Y 0 t, Y t ] a d t (Y t ) a d t (Yt ) = a d t (Y t ) ŷ t (Y t ) Y t ŷ t Y t [Y t + b d t (a d t (Yt ))] [ŷ t + b d t (a d t (ŷ t ))] = Y t ŷ t + b d t (a d t (ŷ t ) + λ(y t ŷ t )) b d t (a d t (ŷ t )) 1

28 b d b t (a) 1 d t (ad t (ŷ t)+λ(y t ŷ t )) b d t (ad t (ŷ t)) a d t (ŷt)+λ(yt ŷt) ad t (ŷt) 1 [Y t + b d t (a d t (Yt ))] [ŷ t + b d t (a d t (ŷ t ))] Y t ŷ t λ(y t ŷ t ) = (Y t ŷ t )(1 λ) 0 g(y) a d t (y) λ(y) (3.14) g(y) y 3.15 E[g(Y t )] = a y t λµ t := g t E[Y t + b d t (λy t + g(y t ))] = µ t + E[b d t (λy t + g(y t ))] b d t b d t (λy t + g(y t )) b d t (λy t + g t ) + b d t (λyt + g t )(g(y t ) g t ) Y t ( ) E[b d t (λy t + g(y t ))] E[b d t (λy t + g t )] + Cov b d t (λyt + g t ), (g(y t ) g t ) b d t bd t (λyt + g t ) Y t g(y t ) g t Y t ( ) Cov b d t (λyt + g t ), (g(y t ) g t ) 0 ( ) E[b d t (λy t + g(y t ))] E[b d t (λy t + g t )] + Cov b d t (λyt + g t ), (g(y t ) g t ) E[b d t (λy t + g t )] E[Y t + b d t (a d t (Y t ))] = E[b d t (λy t + g(y t ))] g(y t ) = g t = a y t λµ t g(y t ) = a d t (Y t ) λy t a d t (Y t ) = a y t + λ(y t µ t ) y a d t (y) = a y t + λ(y µ t) 3 t a t a γ r 3 2

29 4 4 1 t c d t = λ 1 (a 1 t a d t ) a d t d t = λmax( c d t, 0) = max(a d t a 1 t, 0) t = T L t t < T p t p t = max(cd t c L t, 0) N t = max(λ 1 (a 1 t a d t ) λ 1 (a 1 t a L t ), 0) λ 1 (a L t R t) = max(al t a d t, 0) (a L t R t) c e t = max(min(c d t, c L t ), 0) = λ 1 max(min(a 1 t a d t, a 1 t a L t ), 0) = λ 1 (a 1 t min(max(a d t, a L t ), a 1 t ) = λ 1 (a 1 t a e t ) γ k t Y t 3

30 c d t + = e γ(t+ t)c e t + x t Y t + = e γ(t+ t) λ 1 (a 1 t a e t) + µ t + λ 1 (a 1 t e + γ(t+ t) a 1 t ) Y t + = λ 1 [a 1 t (e + γ(t+ t) a e t + λ(y t + µ t +))] = λ 1 (a 1 t a d + t ) + a d t ad t λ 1 λ t < T R t T R T L T R T + λl T T a e T > R T + λl T (A.1) a e T η a e T = η + E[e γ(τ T ) R τ ] (A.2) (1 λ) 100 (3.3) b e T (ae T ) = 1 λ η (A.3) λ R T E[e γ(τ T ) R τ ] (A.4) 4

31 (A.1) (A.4) a e T + be T (ae T ) 1 λ η + E[e γ(τ T ) R τ ] > 1 λ [R T E[e γ(τ T ) R τ ] + λl T ] + E[e γ(τ T ) R τ ] R T + L T l T 1 T 5

32 1) Bruno Biais, Thomas Mariotti: Dynamic Security Design: Convergence to Continuous Time and Asset Pricing Implications, Review of Economic Studies, Vol. 74, No. 2, pp , ) Chiala,N. Garvin, M, J. Vever, J. Valuing Simple Multiple-Exercise Real Optionsin infrastructure Porjects, Journal of Infrastructure Systems, June 2007 pp ) Peter M. DeMarzo, Michael J. Fishman: Optimal Long-Term Financial Contracting, Review of Financial Studies, pp , ) Peter M. DeMarozo, Yuliy Sannikonv, Optimal Security Design and Dynamic Capital Structure in a Continuous-Time Agency Model, Journal of Finance 61: , ) Douglas W. Diamond, Financial Intermediation and Delegated Monitoring Review of Economic Studies 51: ) Peter M. Demarzo, Michael J. Fishman: Agency and Optimal Investment Dynamics. Review of Financial Studies 20: ) Edward J. Green: Lending and the Smoothing of Uninsurable Income, in E. Prescott, and N.Wallace (eds), Contractual Arrangements for Intertemporal Trade, Minneapolis: University of Minnesota Press. 8) Denis Gromb: Renegotiation in Debt Contracts, working paper, MIT. 9) Myerson, R. B.: Bayesian equilibrium and incentive compatibility: An introduction, in J.-J. Laffont (ed.), Advances in Economic Theory: Sixth World Congress, Volume I, Cambridge University Press, ) Jonathan Thomas, Tim Worrall: Income Fluctuation and Asymmetric Information: An Example of a Repeated Principal-Agent Problem, Journal of Economic Theory, 51, ) No.44,

33 12) PFI pp ) PFI Vol.12 pp ) PFI Vo.30 pp.15-30,

34 GCOE GCOE

(1) (Karlan, 2004) (1) (1973) (1978) (1991) (1991) 1

(1) (Karlan, 2004) (1) (1973) (1978) (1991) (1991) 1 2004 1 8 2005 12 17 1 (1) (Karlan, 2004) 2 3 4 5 E-mail: aa37065@mail.ecc.u-tokyo.ac.jp (1) (1973) (1978) (1991) (1991) 1 2 2 2.1 (, 1978, 7 ) (2) (1988) 38 2 (3) (4) (2) (1986) 91 (1996) 2 1 (1993) 1