Arbitrage and Hedging in a non probabilistic framework

Mathematics and Financial Economics 03/2011; 7(1). DOI: 10.1007/s11579-012-0074-5
Source: arXiv


The paper studies the concepts of hedging and arbitrage in a non
probabilistic framework. It provides conditions for non probabilistic arbitrage
based on the topological structure of the trajectory space and makes
connections with the usual notion of arbitrage. Several examples illustrate the
non probabilistic arbitrage as well perfect replication of options under
continuous and discontinuous trajectories, the results can then be applied in
probabilistic models path by path. The approach is related to recent financial
models that go beyond semimartingales, we remark on some of these connections
and provide applications of our results to some of these models.

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    • "The paper concentrates entirely on discrete, non probabilistic, market models extending the model in [11]. The setting could be considered as a discrete version of the non probabilistic, trajectory based, continuoustime models recently introduced in [3] and further developed in [4]. An example is given in Section 4 illustrating a general approach to constructing trajectory sets without using a priori probabilistic assumptions. "
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