The super-replication problem via probabilistic methods
type: Item
instance of: scholarly article
title: The super-replication problem via probabilistic methods
zbMATH Open document ID: 1029.60052
author: Paulius Jakubėnas
author: Shlomo Levental
author: Michał Ryznar
published in: The Annals of Applied Probability
publication date: 2003-11-17T00:00:00Z
review text: This paper deals with finding the minimal investment that is needed, in the presence of transaction costs, to super-replicate options using their underlying financial assets. The goal is to select, from all the portfolios that have values exceeding the payoff associated with the option, the one with the smallest initial value. Exclusively probabilistic methods are used. Both exotic and path-independent European and American options are considered. The main idea is that if an investor can super-replicate an option in a continuous-time model with transaction costs, then it is possible with even smaller initial investment to hedge a perpetual discrete-time related option in a market which is free of transaction costs where prices are martingales. The method is to study in a discrete-time shadow market that is free of transaction costs, where the options are perpetual. The advantage of the approach is that any trading strategies restrictions related to the bankruptcy condition are not imposed. Hedging with unlimited borrowing is allowed and still the best policy is buy-and-hold.
Mathematics Subject Classification ID: 60H30
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 60H05
zbMATH DE Number: 2005176
zbMATH Keywords: transaction costs
zbMATH Keywords: super-replication
zbMATH Keywords: hedging options
zbMATH Keywords: robust method
zbMATH Keywords: buy-and-hold
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1050689602
OpenAlex ID: W2125946349
cites work: DERIVATIVE ASSET PRICING WITH TRANSACTION COSTS1
cites work: The pricing of options and corporate liabilities
cites work: Explicit solution to the multivariate super-replication problem under transaction costs.
cites work: HEDGING AND PORTFOLIO OPTIMIZATION UNDER TRANSACTION COSTS: A MARTINGALE APPROACH12
cites work: A closed-form solution to the problem of super-replication under transaction costs
cites work: A note on super-replicating strategies
cites work: Martingales and stochastic integrals in the theory of continuous trading
cites work: On the possibility of hedging options in the presence of transaction costs
cites work: Q4905685
cites work: There is no nontrivial hedging portfolio for option pricing with transaction costs
DOI: 10.1214/AOAP/1050689602
Recommended article: Q4429139
Recommended article: The multi-dimensional super-replication problem under gamma constraints
Recommended article: The Robust Superreplication Problem: A Dynamic Approach
Recommended article: Erratum: The Robust Superreplication Problem: A Dynamic Approach
Recommended article: Super Solutions of Random Instances of Satisfiability
Recommended article: Superreplication under model uncertainty in discrete time
Recommended article: Explicit solution to the multivariate super-replication problem under transaction costs.
Recommended article: Q3339292
description: scientific article; zbMATH DE number 2005176