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The asymptotic elasticity of utility functions and optimal investment in incomplete markets
The paper studies the problem of maximizing the expected utility of terminal wealth in the framework of a general incomplete semimartingale model of a financial market. We show that the necessary andExpand
Affine Processes and Application in Finance
We provide the definition and a complete characterization of regular affine processes. This type of process unifies the concepts of continuousstate branching processes with immigration andExpand
The fundamental theorem of asset pricing for unbounded stochastic processes
The Fundamental Theorem of Asset Pricing states - roughly speaking - that the absence of arbitrage possibilities for a stochastic process S is equivalent to the existence of an equivalent martingaleExpand
The Mathematics of Arbitrage
A Guided Tour to Arbitrage Theory.- The Story in a Nutshell.- Models of Financial Markets on Finite Probability Spaces.- Utility Maximisation on Finite Probability Spaces.- Bachelier andExpand
The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time
We prove a version of the Fundamental Theorem of Asset Pricing, which applies to Kabanov's approach to foreign exchange markets under transaction costs. The financial market is modelled by a d x dExpand
Optimal investment in incomplete markets when wealth may become negative
This paper accompanies a previous one from 1999 by D. Kramkov and the present author. There, we considered utility functions $U:\R_+ \to \R$ satisfying the Inada conditions $U'(0)=\infty$ andExpand
Law Invariant Risk Measures Have the Fatou Property
S. Kusuoka [K 01, Theorem 4] gave an interesting dual characterizationof law invariant coherent risk measures, satisfying the Fatou property.The latter property was introduced by F. Delbaen [D 02].Expand
Necessary and sufficient conditions in the problem of optimal investment in incomplete markets
Following [10] we continue the study of the problem of expected utility maximization in incomplete markets. Our goal is to nd minimal conditions on a model and a utility function for the validity ofExpand
Optimal Risk Sharing for Law Invariant Monetary Utility Functions
We consider the problem of optimal risk sharing of some given total risk between two economic agents characterized by law-invariant monetary utility functions or equivalently, law-invariant riskExpand