Pricing and hedging in incomplete financial markets

In the practical part, Chapter 4 considers numerical methods for indifference pricing in a stochastic volatility model. In Chapter 5, a feasible procedure is developed for calculating the CVaR price in unit-linked insurance products under an additional assumption. This assumption is relaxed in Chapter 6.

Pricing and Hedging in Incomplete Financial Markets.

In the practical part, Chapter 4 considers numerical methods for indifference pricing in a stochastic volatility model. In Chapter 5, a feasible procedure is developed for calculating the CVaR price in unit-linked insurance products under an additional assumption. This assumption is relaxed in Chapter 6.

Duality Theory for Robust Utility Maximisation

In this paper we present a duality theory for the robust utility maximisation problem in continuous time for utility functions defined on the positive real axis. Our results are inspired by -- and can be seen as the robust analogues of -- the seminal work of Kramkov & Schachermayer [18]. Namely, we show that if the set of attainable trading outcomes and the set of pricing measures satisfy a bipolar relation, then the utility maximisation problem is in duality with a conjugate problem. We further discuss the existence of optimal trading strategies. In particular, our general results include the case of logarithmic and power utility, and they apply to drift and volatility uncertainty

A MODEL-FREE ANALYSIS OF DISCRETE TIME FINANCIAL MARKETS

We discuss fundamental questions of Mathematical Finance such as arbitrage and hedging in the context of a discrete time market with no reference probability. We show how different notions of arbitrage can be studied under the same general framework by specifying a class S of significant sets, and we investigate the richness of the family of martingale measures in relation to the choice of S. We also provide a superhedging duality theorem. We show that the initial cost of the cheapest portfolio that dominates a contingent claim on every possible path, might be strictly greater than the upper bound of the no-arbitrage prices. We therefore characterize the subset of trajectories on which this duality gap disappears and observe how this is related to no-arbitrage considerations. We finally consider the extension of the previous results to markets with frictions