Detecting Type-B Arbitrage with (ADLP) - Practice For type-B arbitrage the following conditions need to be satisfied: Po(y) = Six; < 0, (i) i=0 Esi(w;)x; > 0, j = 1, 2, ..., m, (ii) i=0 > Si(w;)x; > 0 for at least one index j (iii) i=0 We can find such an investment x (if one exists) by solving m ОРТ :3 S{(w;)X; min i=0 subject to E Si(w;)x; > 0, j= 1,2, ..., m. (ADLP) i=0 E sixi <0 i=0 Define OPT = -o if the problem is unbounded
Detecting Type-B Arbitrage with (ADLP) - Practice For type-B arbitrage the following conditions need to be satisfied: Po(y) = Six; < 0, (i) i=0 Esi(w;)x; > 0, j = 1, 2, ..., m, (ii) i=0 > Si(w;)x; > 0 for at least one index j (iii) i=0 We can find such an investment x (if one exists) by solving m ОРТ :3 S{(w;)X; min i=0 subject to E Si(w;)x; > 0, j= 1,2, ..., m. (ADLP) i=0 E sixi <0 i=0 Define OPT = -o if the problem is unbounded
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Transcribed Image Text:Detecting Type-B Arbitrage with (ADLP) - Practice
For type-B arbitrage the following conditions neèd to be satisfied:
Po(y) =
E söx; s0,
(i)
i=0
ES{(w; )x; > 0,
j = 1, 2, ..., m,
(ii)
i=0
in
Es{(w;)x; > 0
for at least one index j
(ii)
i=0
We can find such an investment x (if one exists) by solving
ОРТ
min
-
j=1
i=0
subject to
S;(w;)x; > 0, j = 1, 2, . . . , m.
(ADLP)
i=0
in
Sóx; <0
i=0
Define OPT
= -o if the problem is unbounded
Transcribed Image Text:Consider the linear program from lecture slides for detecting type-B arbitrage in practice. Leave
the constraints unchanged but replace the objective function with
- E a; E, S{ (w;)æ; for some vector a = (a1, ... , am).
For what a does this modified LP have
0o value if and only if type-B arbitrage exists ?
Ο Σ α
= some positive constant
aj 2 0 for all j
aj > 0 for all j
All of the above
O None of the above
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