A duality for robust hedging with proportional transaction costs of pathdependent European options is obtained in a discrete-time financial market with one risky asset. The investor's portfolio consists of a dynamically traded stock and a static position in vanilla options, which can be exercised at maturity. Trading of both options and stock is subject to proportional transaction costs. The main theorem is a duality between hedging and a Monge-Kantorovich-type optimization problem. In this dual transport problem, the optimization is over all probability measures that satisfy an approximate martingale condition related to consistent price systems, in addition to an approximate marginal constraint.
Bibliographical noteFunding Information:
Research of Dolinsky is partly supported by a career integration grant, CIG- 618235 and research of Soner is supported by the European Research Council under the grant 228053-FiRM, by the ETH Foundation, and by the Swiss Finance Institute. The authors would like to thank Lev Buhovsky, Jan Obłój, and Josef Teichmann for insightful discussions and comments.
- Consistent price systems
- European options
- Fundamental theorem of asset pricing
- Optimal transport
- Robust hedging
- Transaction costs
- Weak convergence