Optional decompositions under constraints

Motivated by a hedging problem in mathematical finance, El Karoui and Quenez [7] and Kramkov [14] have developed optional versions of the Doob-Meyer decomposition which hold simultaneously for all equivalent martingale measures. We investigate the general structure of such optional decompositions, both in additive and in multiplicative form, and under constraints corresponding to di_erent classes of equivalent measures. As an application, we extend results of Karatzas and Cvitanic [3] on hedging problems with constrained portfolios

Closed form representations for the minimal hedging portfolios of American type contingent claims

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Construction of an Aggregate Consistent Utility, Without Pareto Optimality. Application to Long-Term Yield Curve Modeling

The aim of this paper is to describe globally the behavior and preferences of heterogeneous agents. Our starting point is the global wealth of the economy, with a given repartition of the wealth among investors, which is not necessarily Pareto optimal. We propose a construction of an aggregate forward utility, market consistent, that aggregates the marginal utility of the heterogeneous agents. This construction is based on the aggregation of the pricing kernels of each investor. As an application we analyze the impact of the heterogeneity and of the global wealth market on the yield curve