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Portfolio Optimization with Different Information Flow recalls the stochastic tools and results concerning the stochastic optimization theory and the enlargement filtration theory.The authors apply the theory of the enlargement of filtrations and solve the optimization problem. Two main types of enlargement of filtration are discussed: initial and progressive, using tools from various fields, such as from stochastic calculus and convex analysis, optimal stochastic control and backward stochastic differential equations.
This theoretical and numerical analysis is applied in different market settings to provide a good basis for the understanding of portfolio optimization with different information flow.
- Presents recent progress of stochastic portfolio optimization with exotic filtrations
- Shows you how to apply the tools of the enlargement of filtrations to resolve the optimization problem
- Uses tools from various fields from enlargement of filtration theory, stochastic calculus, convex analysis, optimal stochastic control, and backward stochastic differential equations
Graduate students, researchers, portfolio managers and academics worldwide working in all sub-disciplines of economics, mathematics and finance
1: Optimization Problems
- 1.1 Portfolio optimization problem
- 1.2 Duality approach
- 1.3 Dynamic programming principle
- 1.4 Several explicit examples
- 1.5 Brownian-Poisson filtration with general utility weights
2: Enlargement of Filtration
- 2.1 Conditional law and density hypothesis
- 2.2 Initial enlargement of filtration
- 2.3 Progressive enlargement of filtration
3: Portfolio Optimization with Credit Risk
- 3.1 Model setup
- 3.2 Direct method with the logarithmic utility
- 3.3 Optimization for standard investor: power utility
- 3.4 Decomposition method with the exponential utility
- 3.5 Optimization with insider’s information
- 3.6 Numerical illustrations
4: Portfolio Optimization with Information Asymmetry
- 4.1 The market
- 4.2 Optimal strategies in some examples of side-information
- 4.3 Numerical illustrations
- No. of pages:
- © ISTE Press - Elsevier 2017
- 1st February 2017
- ISTE Press - Elsevier
- Hardcover ISBN:
- eBook ISBN:
Caroline Hillairet is a Professor at ENSAE ParisTech, University Paris Saclay, CREST in France, where she is in charge of the actuarial science program. Her research interests include information asymmetry and enlargement of filtrations, portfolio optimization, credit risk, and the financial issues of longevity risk.
Assistant Professor, CMAP Ecole Polytechnique
Ying Jiao is a Professor at University of Lyon in France. Her research interests include mathematical finance, the general theory of processes and enlargement of filtrations, and Stein's method.
ISFA Université Lyon 1