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E-grāmata: Portfolio Optimization with Different Information Flow

(Assistant Professor, CMAP Ecole Polytechnique), (ISFA Université Lyon 1)
  • Formāts: EPUB+DRM
  • Izdošanas datums: 10-Feb-2017
  • Izdevniecība: ISTE Press Ltd - Elsevier Inc
  • Valoda: eng
  • ISBN-13: 9780081011775
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Portfolio Optimization with Different Information FlowPalielināt
  • Formāts: EPUB+DRM
  • Izdošanas datums: 10-Feb-2017
  • Izdevniecība: ISTE Press Ltd - Elsevier Inc
  • Valoda: eng
  • ISBN-13: 9780081011775
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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.

Papildus informācija

This important work provides an overview of the role and impact of different information flow in the classical problem of optimal investment, exploring both a default free market and a defaultable market
Introduction vii
Chapter 1 Optimization Problems
1(44)
1.1 Portfolio optimization problem
2(9)
1.1.1 Portfolio value
2(3)
1.1.2 Optimization problem
5(2)
1.1.3 Examples of utility functions
7(4)
1.2 Duality approach
11(12)
1.2.1 Change of probability measures
13(1)
1.2.2 Dual optimization problem
13(5)
1.2.3 Examples
18(5)
1.3 Dynamic programming principle
23(5)
1.4 Several explicit examples
28(11)
1.4.1 Brownian setting
28(5)
1.4.2 Brownian setting with additive utility weight
33(6)
1.5 Brownian-Poisson filtration with general utility weights
39(6)
1.5.1 Logarithmic utility
42(3)
Chapter 2 Enlargement of Filtration
45(26)
2.1 Conditional law and density hypothesis
46(5)
2.2 Initial enlargement of filtration
51(9)
2.2.1 Martingales of the enlarged filtration
52(5)
2.2.2 Example of a Brownian-Poisson filtration and information drift
57(1)
2.2.3 Noisy initial enlargements
58(2)
2.3 Progressive enlargement of filtration
60(11)
2.3.1 Conditional expectation
62(2)
2.3.2 Right-continuity of the enlarged filtration
64(2)
2.3.3 Martingale characterization
66(3)
2.3.4 Dynamic enlargement with a process
69(2)
Chapter 3 Portfolio Optimization with Credit Risk
71(70)
3.1 Model setup
73(8)
3.1.1 Preliminaries
73(6)
3.1.2 The optimization problem
79(2)
3.2 Direct method with the logarithmic utility
81(2)
3.3 Optimization for standard investor: power utility
83(23)
3.3.1 Decomposition of the optimization problem
84(4)
3.3.2 Solution to the after-default optimization problem
88(3)
3.3.3 Resolution of the before-default optimization problem
91(10)
3.3.4 Example and numerical illustrations
101(5)
3.4 Decomposition method with the exponential utility
106(7)
3.5 Optimization with insider's information
113(20)
3.5.1 Insider's optimization problem
114(5)
3.5.2 Decomposition of the optimization problem
119(8)
3.5.3 The logarithmic utility case
127(2)
3.5.4 Power utility case
129(4)
3.6 Numerical illustrations
133(8)
Chapter 4 Portfolio Optimization with Information Asymmetry
141(24)
4.1 The market
143(4)
4.1.1 Risk neutral probabilities measures for insider
145(2)
4.1.2 Solution of the optimization problem
147(1)
4.2 Optimal strategies in some examples of side-information
147(10)
4.2.1 Initial strong insider
147(2)
4.2.2 There exist i, 1 ≤ i ≤ d, such that L = 1[ a,b](Si/T'), 0 < a < b
149(6)
4.2.3 L = log(Si1/T') -- log(Si2/T')
155(2)
4.3 Numerical illustrations
157(8)
4.3.1 L = 1[ a,b](S1/T'), 0 < a < b
158(1)
4.3.2 L = log(S1/T') -- log(S2/T')
159(1)
4.3.3 L = 1[ a,b](S1/T')
160(1)
4.3.4 L = log(S1/T') -- log(S2/T')
160(5)
Bibliography 165(10)
Index 175
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. 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.
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