HEDGING UNDER ARBITRAGE
By J. Ruf. 2010
101 citations recorded by the source corpus.
It is shown that delta hedging provides the optimal trading strategy in terms of minimal required initial capital to replicate a given terminal payoff in a continuous‐time Markovian context. This holds true in market models in which no equivalent local martingale measure exists but only a square‐integrable market price of risk. A new probability measure is constructed, which takes the place of an equivalent local martingale measure. To ensure the existence of the delta hedge, sufficient conditions are derived for the necessary differentiability of expectations indexed over the initial market configuration. The phenomenon of “bubbles,” which has recently been frequently discussed in the academic literature, is a special case of the setting in this paper. Several examples at the end illustrate the techniques described in this work.
Subfields: Finance, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/6d9972cfce4ffc537bcac544d3aad3350aed392b
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Finance
- Ioannis Karatzas
- Daniel Fernholz
- J. Ruf
- Nicolas Perkowski
- David J. Promel
- Soumik Pal
- Marcel Nutz
- Massimiliano Gubinelli
In Management Science and Operations Research
- Ioannis Karatzas
- J. Ruf
- Nicolas Perkowski
- David J. Promel
- Daniel Fernholz
- Marcel Nutz
- Gordan Zitkovic
- Constantinos Kardaras
Citations in the corpus
- Distribution of the time to explosion for one-dimensional diffusions (2013, background): “This version can be considered a “weak” result, as it provides a distributional identity; Ruf (2013b) and Larsson and Ruf (2014) use a related “strong” (i.e., pathwise) version to provide a proof of the sufficiency of the Novikov and Kazamaki criteria for the martingale property of stochastic…”
- Optimal arbitrage under model uncertainty. (2011, background): “(7.6) For justification of the claims made in this subsection, we refer to Section 7 in Fernholz and Karatzas (2010a), as well as Delbaen and Schachermayer (1995a), Pal and Protter (2010) and Ruf (2011)—in addition, of course, to the seminal work by Föllmer (1972, 1973).”
- Pathwise stochastic integrals for model free finance (2013, background): “See [36] for the case of continuous S, and [23] for the general case.”