Note on 'Improved Frechet Bounds and Model-Free Pricing of Multi-Asset Options' by Tankov (2011)

2012 ◽  
Author(s):  
Carole Bernard ◽  
Xiao Jiang ◽  
Steven Vanduffel
Keyword(s):  
Model Free ◽  
Fréchet Bounds

scholarly journals Improved Fréchet Bounds and Model-Free Pricing of Multi-Asset Options

2011 ◽  
Vol 48 (02) ◽  
pp. 389-403 ◽  
Author(s):  
Peter Tankov
Keyword(s):  
Random Vector ◽  
Partial Information ◽  
Dependence Structure ◽  
Extra Information ◽  
Model Free ◽  
Compute Model ◽  
Concordance Order ◽  
Fréchet Bounds

Improved bounds on the copula of a bivariate random vector are computed when partial information is available, such as the values of the copula on a given subset of [0, 1]2, or the value of a functional of the copula, monotone with respect to the concordance order. These results are then used to compute model-free bounds on the prices of two-asset options which make use of extra information about the dependence structure, such as the price of another two-asset option.

scholarly journals A Note on ‘Improved Fréchet Bounds and Model-Free Pricing of Multi-Asset Options’ by Tankov (2011)

2012 ◽  
Vol 49 (3) ◽  
pp. 866-875 ◽  
Author(s):  
Carole Bernard ◽  
Xiao Jiang ◽  
Steven Vanduffel
Keyword(s):  
Lower Bound ◽  
Portfolio Selection ◽  
Sufficient Conditions ◽  
Optimal Investment ◽  
Sufficient Condition ◽  
Investment Strategies ◽  
Model Free ◽  
State Dependent ◽  
Bivariate Copula ◽  
Fréchet Bounds

Tankov (2011) improved the Fréchet bounds for a bivariate copula when its values on a compact subset of [0, 1]2 are given. He showed that the best possible bounds are quasi-copulas and gave a sufficient condition for these bounds to be copulas. In this note we give weaker sufficient conditions to ensure that the bounds are copulas. We also show how this can be useful in portfolio selection. It turns out that finding a copula as a lower bound plays a key role in determining optimal investment strategies explicitly for investors with some type of state-dependent constraints.

scholarly journals A Note on ‘Improved Fréchet Bounds and Model-Free Pricing of Multi-Asset Options’ by Tankov (2011)

2012 ◽  
Vol 49 (03) ◽  
pp. 866-875 ◽  
Author(s):  
Carole Bernard ◽  
Xiao Jiang ◽  
Steven Vanduffel
Keyword(s):  
Lower Bound ◽  
Portfolio Selection ◽  
Sufficient Conditions ◽  
Optimal Investment ◽  
Sufficient Condition ◽  
Investment Strategies ◽  
Model Free ◽  
State Dependent ◽  
Bivariate Copula ◽  
Fréchet Bounds

Tankov (2011) improved the Fréchet bounds for a bivariate copula when its values on a compact subset of [0, 1]2 are given. He showed that the best possible bounds are quasi-copulas and gave a sufficient condition for these bounds to be copulas. In this note we give weaker sufficient conditions to ensure that the bounds are copulas. We also show how this can be useful in portfolio selection. It turns out that finding a copula as a lower bound plays a key role in determining optimal investment strategies explicitly for investors with some type of state-dependent constraints.

scholarly journals Improved Fréchet Bounds and Model-Free Pricing of Multi-Asset Options

2011 ◽  
Vol 48 (2) ◽  
pp. 389-403 ◽  
Author(s):  
Peter Tankov
Keyword(s):  
Random Vector ◽  
Partial Information ◽  
Dependence Structure ◽  
Extra Information ◽  
Model Free ◽  
Compute Model ◽  
Concordance Order ◽  
Fréchet Bounds

Improved bounds on the copula of a bivariate random vector are computed when partial information is available, such as the values of the copula on a given subset of [0, 1]2, or the value of a functional of the copula, monotone with respect to the concordance order. These results are then used to compute model-free bounds on the prices of two-asset options which make use of extra information about the dependence structure, such as the price of another two-asset option.

Representation, abstraction, and simple-minded sophisticates

2020 ◽  
Vol 43 ◽  
Author(s):  
Peter Dayan
Keyword(s):  
Decision Theory ◽  
Predictive Coding ◽  
Bayesian Decision Theory ◽  
Bayesian Decision ◽  
Model Based ◽  
Model Free

Abstract Bayesian decision theory provides a simple formal elucidation of some of the ways that representation and representational abstraction are involved with, and exploit, both prediction and its rather distant cousin, predictive coding. Both model-free and model-based methods are involved.

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