A new view on the Fundamental Theorem of Asset
Pricing for Large Financial Markets
Cuchiero C., Klein I., Teichmann J.
Discussion
XVI Workshop on Quantitative Finance - Parma 2015
Cuchiero C.
FTAP for Large Markets
30-01-15
1/4
Contribution/1
The aim is to model financial markets with infinite number of assets.
Result in the literature:
NAFL⇐⇒ EMS’
Trading strategies: portfolios of a finite number of stocks among the
infinite number which are available .
Results are based on weak* closure of super-replicable contingent
claims: C.
Cuchiero C.
FTAP for Large Markets
30-01-15
2/4
Contribution/1
The aim is to model financial markets with infinite number of assets.
Result in the literature:
NAFL⇐⇒ EMS’
Trading strategies: portfolios of a finite number of stocks among the
infinite number which are available .
Results are based on weak* closure of super-replicable contingent
claims: C.
Contribution from this paper:
NAFLVR⇐⇒ EMS
Trading strategies: generalized admissible portfolios. It involves the
closure of the portfolio values in the Emery topology.
Results are based on k · k∞ closure of super-replicable contingent
claims: C .
Cuchiero C.
FTAP for Large Markets
30-01-15
2/4
Contribution/2
The paper provides the following contributions:
Provides a notion of NAFLVR related to k · k∞ closure which has a
more meaningful financial interpretation.
Cuchiero C.
FTAP for Large Markets
30-01-15
3/4
Contribution/2
The paper provides the following contributions:
Provides a notion of NAFLVR related to k · k∞ closure which has a
more meaningful financial interpretation.
It expand on the previous Theorem by showing that these concepts
are equivalent.
Cuchiero C.
FTAP for Large Markets
30-01-15
3/4
Contribution/2
The paper provides the following contributions:
Provides a notion of NAFLVR related to k · k∞ closure which has a
more meaningful financial interpretation.
It expand on the previous Theorem by showing that these concepts
are equivalent.
It has been proved in a very general setting able to incorporate many
interesting cases.
Cuchiero C.
FTAP for Large Markets
30-01-15
3/4
Contribution/2
The paper provides the following contributions:
Provides a notion of NAFLVR related to k · k∞ closure which has a
more meaningful financial interpretation.
It expand on the previous Theorem by showing that these concepts
are equivalent.
It has been proved in a very general setting able to incorporate many
interesting cases.
Provides an interpretation to the assumption EMS used by other
authors (e.g. De Donno et al.) for super-hedging and utility
maximization.
Cuchiero C.
FTAP for Large Markets
30-01-15
3/4
Contribution/2
The paper provides the following contributions:
Provides a notion of NAFLVR related to k · k∞ closure which has a
more meaningful financial interpretation.
It expand on the previous Theorem by showing that these concepts
are equivalent.
It has been proved in a very general setting able to incorporate many
interesting cases.
Provides an interpretation to the assumption EMS used by other
authors (e.g. De Donno et al.) for super-hedging and utility
maximization.
Compare the notion of NAFLVR with other possible condition and
discuss the relation with EMS.
Cuchiero C.
FTAP for Large Markets
30-01-15
3/4
Contribution/2
The paper provides the following contributions:
Provides a notion of NAFLVR related to k · k∞ closure which has a
more meaningful financial interpretation.
It expand on the previous Theorem by showing that these concepts
are equivalent.
It has been proved in a very general setting able to incorporate many
interesting cases.
Provides an interpretation to the assumption EMS used by other
authors (e.g. De Donno et al.) for super-hedging and utility
maximization.
Compare the notion of NAFLVR with other possible condition and
discuss the relation with EMS.
Characterize NAFLVR in terms of NUPBR + NA.
Cuchiero C.
FTAP for Large Markets
30-01-15
3/4
Questions
The main result is based on k · k∞ closure which has clear
interpretation. Nevertheless the generalized strategies are construct
by taking limits in the Emery topology.
Can you comment on the interpretation of these strategies?
What types of convergence are implied?
Cuchiero C.
FTAP for Large Markets
30-01-15
4/4
Questions
The main result is based on k · k∞ closure which has clear
interpretation. Nevertheless the generalized strategies are construct
by taking limits in the Emery topology.
Can you comment on the interpretation of these strategies?
What types of convergence are implied?
What is the role of the “concatenation property”. Is it just a technical
requirement or it does exclude significant classes of strategies?
Cuchiero C.
FTAP for Large Markets
30-01-15
4/4
Questions
The main result is based on k · k∞ closure which has clear
interpretation. Nevertheless the generalized strategies are construct
by taking limits in the Emery topology.
Can you comment on the interpretation of these strategies?
What types of convergence are implied?
What is the role of the “concatenation property”. Is it just a technical
requirement or it does exclude significant classes of strategies?
The most natural set of strategies seems to be
[[
λχn1
λ n≥1
but the k · k∞ closure turns out to be not sufficent for EMS. Would it
be worthy to weaken the EMS property?
Cuchiero C.
FTAP for Large Markets
30-01-15
4/4