.
, , W. , (), L ≤ W. , , , q. nq, n . q.
, (1) . q:
Max [ p U (W L pq + q) + (1 p) U (W pq)]
Q
, .. q :
pU' (W L pq* + q*) (1 p) + (1 p) U'(W pq*) (- p) = 0
q* q.
:
U'(W L - pq* + q*) / U'(W - pq*) = (l - p) p / p (l - p)
U, q*.
, , .
, πq - q. , nq. :
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p (pq - q) + (1 p) pq = ppq - pq + pq ppq = q (p p)
- .
, , .. ∂(π - ) = 0 , π →.
, L . = , :
U'[(W L) + (1 p) q*] = U'(W pq*)
, U'(W) < 0, :
W L + (1 p) q* = W pq*
- L + q*- pq* = - pq*.
q* = L.
:
, .. (, , , , ..);
, .. , , ;
, .. , . ;
, .. , . , .
, . - , (. 929 ).
. : , , , , , . , , , .
, , . , . , , .
.
, / 12 =
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D, .. (1) = (1 +0), - (2) = (1 + D) 2, k - - (k) = (1 + D) k, k = 1, 2,... 12.
- .
0 (k)= 0 - (1) (2) -... - (k)
( ) k- .
- (1) + (2) +... + (12) = S(12), k = 12: (12) = 0.
, - (12). = (k) , . 0 (k) (k). : (k) = = (k - 1) - (k) + (k).
(k), .
, .. V(k) V(k) ∙ (1 + ), - , - , k = 1, 2,..., 12.
(k) = (k - 1) - (k) + V(k)(1 + A).
V(k).
V(k) , , .. V(k) , - V(k) , B(1).
, V(k) = - B(1).
, :
B(1) + ( - B(1)).
, - :
P(1) = [ B(1)] ∙ (1 + ).
V(2), , (2), .. (1) B(2) + (P(1) (2)): , .
P(2) = [P(1) (2)] (1 + ).
:
(2) = [(k - 1) (k)] ∙ (1 + ), = 1, 2,..., 12.
, k- , . . .
- , P(12) = , .
. , , , , , , . . .
, $ , , , e $1. $ , .
, :
- T (), . ;
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- ƒ (). ;
- M / (1 + r s,) T (0), , r (r $ ). T :
$ = (1 + rp) T: e(0) (1+ r$) T (.).
;
- (). , .
- , .
, 6 . $10 000 6 . $1 . . , 5,5 . $1, $10000 6 . $1.
- .
, . $ 10 000 6 . $ 1 , , , 6,5 . $1, , , 5,5 . $1.
. . t = 0, (0) 6,4 . $1. ( = 6 .) $1000. ( ) e = 10%, ( ) r s = 6 %.
, $ 1000 e(T) - 6,6 . $1 $1000 () = 6,6 . $1. 200 .
. ()
πe= MS(e(T)- e0).
πe , . , :
= 1000-((T) - 6,4).
:
MS(eƒ(T) - e(T)).
πƒ , . , :
πƒ = 1000 (6,60 - (T)) .
1+r e
π = M S {e(0) --------- - e(T)}
1+r s
π , Ms , Ms 0, T Ms .
, : π = 1000 ∙ (6,64151 - (T)) . :
π0 = - P + max {0, M S (e 0 (T) - e 0 (T)}
π0 , () .
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, :
Max(0,66 e(T)).
π0 = - 200. + $1000 ----------------------------
$
. , , .
1. .
2. .
3. .
4. ?
5. , .
6. ?
7. ?
8. , .
9. .
10. , .
11. .
12. 600 000 . , 700 000 . , 20%? 12%. . , ? : .
13. NPV 10% , 10% , 5%.
14. .
15. ( ) .
16. . 28 . $1. $1000. ( ) 10%, ( ) 6%. $ 1000 28,8 . $1, $1000 - 28,9 . $1. 1500 . 15%. , , , .
5.
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