The DOI matches its Crossref record; 17 of the 17 references it cites were found in a registry or an index.
HEDGING AND PORTFOLIO OPTIMIZATION UNDER TRANSACTION COSTS: A MARTINGALE APPROACH12
Abstract
We derive a formula for the minimal initial wealth needed to hedge an arbitrary contingent claim in a continuous‐time model with proportional transaction costs; the expression obtained can be interpreted as the supremum of expected discounted values of the claim, over all (pairs of) probability measures under which the “wealth process” is a supermartingale. Next, we prove the existence of an optimal solution to the portfolio optimization problem of maximizing utility from terminal wealth in the same model, we also characterize this solution via a transformation to a hedging problem: the optimal portfolio is the one that hedges the inverse of marginal utility evaluated at the shadow state‐price density solving the corresponding dual problem, if such exists. We can then use the optimal shadow state‐price density for pricing contingent claims in this market. the mathematical tools are those of continuous‐time martingales, convex analysis, functional analysis, and duality theory.
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Cites
The pricing of options and corporate liabilities
Black, F., & Scholes, M. (1973) · Journal of Political Economy · doi:10.1086/260062 · Cited by 29,074
Brownian Motion and Stochastic Calculus
(2007) · Springer Finance · doi:10.1007/978-1-84628-696-4_13 · Cited by 7,422
Theory of rational option pricing
Merton, R. C. (2005) · Theory of Valuation · doi:10.1142/9789812701022_0008 · Cited by 7,161
Stochastic Integration and Differential Equations
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Convex Analysis and Variational Problems
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Martingales and stochastic integrals in the theory of continuous trading
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A Course in Probability Theory
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Brownian Motion and Stochastic Calculus
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Self-citationPortfolio Selection with Transaction Costs
Davis, M. H. A., & Norman, A. R. (1990) · Mathematics of Operations Research · doi:10.1287/moor.15.4.676 · Cited by 1,311
Option Pricing and Replication with Transactions Costs
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Cited by
LIBOR and swap market models and measures
Jamshidian, F. (1997) · Finance and Stochastics · doi:10.1007/s007800050026 · Cited by 746
Markowitz Revisited: Mean-Variance Models in Financial Portfolio Analysis
Steinbach, M. C. (2001) · SIAM Review · doi:10.1137/s0036144500376650 · Cited by 382
Metadata
- Authors
- Cvitanić, J., & Karatzas, I.
- Venue
- Mathematical Finance
- Publisher
- Wiley
- Published
- 1996-04
- Volume
- 6
- Issue
- 2
- Pages
- 133-165
- ISSN
- 0960-1627 (ISSN-L)
- 1467-9965
- OpenAlex
- W2021355027
- Cited by
- 317
- References
- 17
- FWCI
- 11.65
- Type
- journal article
- Language
- en
- Open access
- closed
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- Cvitanić, J., & Karatzas, I. (1996). HEDGING AND PORTFOLIO OPTIMIZATION UNDER TRANSACTION COSTS: A MARTINGALE APPROACH12. Mathematical Finance. https://doi.org/10.1111/j.1467-9965.1996.tb00075.x
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