The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 25, Number 2 (2015), 823-859.
Arbitrage and duality in nondominated discrete-time models
We consider a nondominated model of a discrete-time financial market where stocks are traded dynamically, and options are available for static hedging. In a general measure-theoretic setting, we show that absence of arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of martingale measures. In the arbitrage-free case, we show that optimal superhedging strategies exist for general contingent claims, and that the minimal superhedging price is given by the supremum over the martingale measures. Moreover, we obtain a nondominated version of the Optional Decomposition Theorem.
Ann. Appl. Probab., Volume 25, Number 2 (2015), 823-859.
First available in Project Euclid: 19 February 2015
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Bouchard, Bruno; Nutz, Marcel. Arbitrage and duality in nondominated discrete-time models. Ann. Appl. Probab. 25 (2015), no. 2, 823--859. doi:10.1214/14-AAP1011. https://projecteuclid.org/euclid.aoap/1424355131