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A Unified Characterization of π-Optimal and Minimal Entropy Martingale Measures by Semimartingale Backward Equations
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M. Mania
Published/Copyright:
March 3, 2010
Abstract
We give a unified characterization of π-optimal martingale measures for π β [0, β) in an incomplete market model, where the dynamics of asset prices are described by a continuous semimartingale. According to this characterization the variance-optimal, the minimal entropy and the minimal martingale measures appear as the special cases π = 2, π = 1 and π = 0 respectively. Under assumption that the Reverse HΓΆlder condition is satisfied, the continuity (in πΏ1 and in entropy) of densities of π-optimal martingale measures with respect to π is proved.
Key words and phrases:: Backward semimartingale equation; π-optimal martingale measure; minimal entropy martingale measure; contingent claim pricing
Received: 2002-12-15
Published Online: 2010-03-03
Published in Print: 2003-June
Β© Heldermann Verlag
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- On the Dimension Modulo Classes of Topological Spaces and Free Topological Groups
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- Dynamic Programming and Mean-Variance Hedging in Discrete Time
- Extending Quasi-Invariant Measures by Using Subgroups of a Given Group
- Representation of Solutions of Some Boundary Value Problems of Elasticity by a Sum of the Solutions of Other Boundary Value Problems
- General π-Estimators in the Presence of Nuisance Parameters. Skew Projection Technique
- A Unified Characterization of π-Optimal and Minimal Entropy Martingale Measures by Semimartingale Backward Equations
- On the Existence of Continuous Modifications of Vector-Valued Random Fields
- Weak Convergence of a Dirichlet-Multinomial Process
- Time-Dependent Barrier Options and Boundary Crossing Probabilities
- On Separation Properties for Families of Probability Measures
- Oscillation Theorems of Nonlinear Difference Equations of Second Order
- On Bounds for the Characteristic Functions of Some Degenerate Multidimensional Distributions
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Keywords for this article
Backward semimartingale equation;
π-optimal martingale measure;
minimal entropy martingale measure;
contingent claim pricing
Articles in the same Issue
- On ARU-Resolutions of Uniform Spaces
- On the Dimension Modulo Classes of Topological Spaces and Free Topological Groups
- On the Uniform Convergence and πΏ-Convergence of Double Fourier Series with Respect to the WalshβKaczmarz System
- Dynamic Programming and Mean-Variance Hedging in Discrete Time
- Extending Quasi-Invariant Measures by Using Subgroups of a Given Group
- Representation of Solutions of Some Boundary Value Problems of Elasticity by a Sum of the Solutions of Other Boundary Value Problems
- General π-Estimators in the Presence of Nuisance Parameters. Skew Projection Technique
- A Unified Characterization of π-Optimal and Minimal Entropy Martingale Measures by Semimartingale Backward Equations
- On the Existence of Continuous Modifications of Vector-Valued Random Fields
- Weak Convergence of a Dirichlet-Multinomial Process
- Time-Dependent Barrier Options and Boundary Crossing Probabilities
- On Separation Properties for Families of Probability Measures
- Oscillation Theorems of Nonlinear Difference Equations of Second Order
- On Bounds for the Characteristic Functions of Some Degenerate Multidimensional Distributions
- Estimates of Fourier Coefficients
- On Approximate Large Deviations for 1D Diffusion
