Duality Links between Portfolio Optimization and Derivative Pricing

This paper establishes links between approaches to portfolio optimization and derivative pricing as to be found in He & Pearson (1991), Karatzas (1996), Pliska (1997), Föllmer & Schweizer (1989), Schweizer (1995), Davis (1997), Fritelli & Bellini (1997), and Kallsen (1998) in a finite market setting. We show that expected utility maximization problems are related in a natural way to the choice of an equivalent martingale measure (or a similar object). This measure leads to so-called neutral derivative prices: Introduction of arbitrary derivatives at these prices does not affect the optimality of a portfolio. Moreover, we suggest a way to derivative valuation that is consistent with initially observed real market prices.