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Table of contents
Remerciements
Introduction générale
Grossissement de filtration en temps discret
Prime d’indifférence de contrats d’assurance vie
Équations différentielles stochastiques rétrogrades, grossissement de filtration et prix d’indifférence de l’information
Équations différentielles stochastiques rétrogrades avancées
1 Enlargement of filtration in discrete time
1.1 Definitions, notation and some important results
1.1.1 Basic results
1.1.2 Arbitrage
1.1.3 Filtration enlargement
1.2 Initial enlargement
1.2.1 Random walk bridge
1.2.2 Initial enlargement with a Z-valued random variable
1.2.3 Arbitrages
1.3 Progressive enlargement
1.3.1 Definitions and first results
1.3.2 Some particular random times
1.3.3 Immersion setting
1.3.4 Representation Theorem
1.3.5 Equivalent probability measures
1.3.6 Cox model
1.3.7 Arbitrages
1.3.8 Construction of from a given supermartingale
2 BSDEs and variable annuities
2.1 Model for variable annuities
2.1.1 The financial market model
2.1.2 Exit time of a variable annuity policy
2.2 Indifference fee rate for variable annuities
2.2.1 Indifference pricing
2.2.2 Utility maximization without variable annuities
2.2.3 Utility maximization with variable annuities
2.2.4 Indifference fee rate
2.2.5 Indifference fee rates for a policyholder
2.2.6 Simulations
2.3 Variable Annuities pricing in the worst case
2.3.1 GMDB and GMLB contracts
2.3.2 Utility maximization and indifference pricing
2.3.3 Simulations
Appendix
2.3.4 Utility maximization between T ^ and T
2.3.5 Proof of Lemma 2.2.7
3 BSDEs, filtration enlargement and IPI
3.1 BSDEs in different filtrations
3.1.1 Projection of the solution of a BSDE
3.1.2 Projection of the driver of a BSDE
3.2 Indifference price of information
3.2.1 Financial market and probability space
3.2.2 Utility maximization
3.2.3 Indifference price of information
4 Some existence results for ABSDEs
4.1 Framework
4.2 ABSDE with jump of type (4.0.1)
4.2.1 Study of the Equation (4.2.4)
4.2.2 Study of the Equation (4.2.5)
4.2.3 Integrability of the solutions
4.2.4 Uniqueness of the solution
4.3 ABSDE with jump of type (4.0.2)
4.3.1 Study of the Equation (4.3.2)
4.3.2 Study of the Equation (4.3.3)
