Section: New Results

Utility maximization and Arbitrage Theory

Participants : Claudio Fontana, Bernt Øksendal, Agnès Sulem.

B. Øksendal and A. Sulem have contributed to the issue of robust utility maximization in jump diffusion markets via a stochastic maximum approach and the links with robust duality [53] .

In the period January - October 2013, the main subject of investigation of C. Fontana has been arbitrage theory, with a special emphasis on no-arbitrage conditions weaker than the classical notion of No Free Lunch with Vanishing Risk (NFLVR). In particular, in the context of financial market models based on diffusion processes (see [35] ), we have provided a characterization of several no-arbitrage conditions as well as a generalization of the second fundamental theorem of asset pricing. In the context of jump-diffusion models under partial information (see [25] ), we have studied the relation between market viability (in the sense of solvability of portfolio optimization problems) and the existence of a martingale measure given by the marginal utility of terminal wealth, without a-priori assuming no-arbitrage restrictions on the model. Finally, in the paper [41] , we have provided a critical analysis of the paper Arbitrage, Approximate Arbitrage and the Fundamental Theorem of Asset Pricing (Wong & Heyde, 2010), where the authors aim at proposing an original and simple proof of the fundamental theorem of asset pricing in the context of incomplete diffusion-based models. We have shown that the method of Wong & Heyde (2010) can only work in the well-known case of complete markets, exhibiting an explicit counterexample.