%PDF-1.4 % 5 0 obj << /S /GoTo /D (chapter*.2) >> endobj 8 0 obj (INTRODUCTION G\311N\311RALE ) endobj 9 0 obj << /S /GoTo /D (section.0.1) >> endobj 12 0 obj (0.1 Maximisation d'utilit\351 dans un mod\350le avec d\351fauts) endobj 13 0 obj << /S /GoTo /D (subsection.0.1.1) >> endobj 16 0 obj (0.1.1 Maximisation de la fonction d'utilit\351 exponentielle et prix d'indiff\351rence dans un march\351 avec d\351faut) endobj 17 0 obj << /S /GoTo /D (subsection.0.1.2) >> endobj 20 0 obj (0.1.2 Optimisation de portefeuille dans un march\351 avec d\351faut sous information totale/partielle) endobj 21 0 obj << /S /GoTo /D (section.0.2) >> endobj 24 0 obj (0.2 Grossissement progressif de filtrations et EDSR \340 sauts) endobj 25 0 obj << /S /GoTo /D (section.0.3) >> endobj 28 0 obj (0.3 Mod\351lisation du spread bid-ask) endobj 29 0 obj << /S /GoTo /D (part.1) >> endobj 32 0 obj (I MAXIMIZATION OF UTILITY IN AN INCOMPLETE MARKET WITH DEFAULTS AND TOTAL/PARTIAL INFORMATION) endobj 33 0 obj << /S /GoTo /D (chapter.1) >> endobj 36 0 obj (1 Exponential utility maximization) endobj 37 0 obj << /S /GoTo /D (section.1.1) >> endobj 40 0 obj (1.1 Introduction) endobj 41 0 obj << /S /GoTo /D (section.1.2) >> endobj 44 0 obj (1.2 The market model) endobj 45 0 obj << /S /GoTo /D (section.1.3) >> endobj 48 0 obj (1.3 Strategies valued in a compact set) endobj 49 0 obj << /S /GoTo /D (section.1.4) >> endobj 52 0 obj (1.4 The non constrained case) endobj 53 0 obj << /S /GoTo /D (subsection.1.4.1) >> endobj 56 0 obj (1.4.1 The set of admissible strategies) endobj 57 0 obj << /S /GoTo /D (subsection.1.4.2) >> endobj 60 0 obj (1.4.2 Characterization of the dynamic value function as the maximal subsolution of a BSDE) endobj 61 0 obj << /S /GoTo /D (section.1.5) >> endobj 64 0 obj (1.5 Approximation of the value function) endobj 65 0 obj << /S /GoTo /D (section.1.6) >> endobj 68 0 obj (1.6 Case of bounded coefficients) endobj 69 0 obj << /S /GoTo /D (section.1.7) >> endobj 72 0 obj (1.7 Coefficients satisfying some integrability conditions) endobj 73 0 obj << /S /GoTo /D (subsection.1.7.1) >> endobj 76 0 obj (1.7.1 Case of strategies valued in a convex-compact set) endobj 77 0 obj << /S /GoTo /D (subsection.1.7.2) >> endobj 80 0 obj (1.7.2 The non constrained case) endobj 81 0 obj << /S /GoTo /D (section.1.8) >> endobj 84 0 obj (1.8 Indifference pricing) endobj 85 0 obj << /S /GoTo /D (section.1.9) >> endobj 88 0 obj (1.9 Generalizations) endobj 89 0 obj << /S /GoTo /D (subsection.1.9.1) >> endobj 92 0 obj (1.9.1 Several default times and several stocks) endobj 93 0 obj << /S /GoTo /D (subsection.1.9.2) >> endobj 96 0 obj (1.9.2 Poisson jumps) endobj 97 0 obj << /S /GoTo /D (section.1.10) >> endobj 100 0 obj (1.10 Appendix) endobj 101 0 obj << /S /GoTo /D (subsection.1.10.1) >> endobj 104 0 obj (1.10.1 Essential supremum) endobj 105 0 obj << /S /GoTo /D (subsection.1.10.2) >> endobj 108 0 obj (1.10.2 A classical lemma of analysis) endobj 109 0 obj << /S /GoTo /D (subsection.1.10.3) >> endobj 112 0 obj (1.10.3 Proof of the closedness by binding of A') endobj 113 0 obj << /S /GoTo /D (subsection.1.10.4) >> endobj 116 0 obj (1.10.4 Proof of the existence of a c\340d-l\340g modification of \(Jt\)) endobj 117 0 obj << /S /GoTo /D (subsection.1.10.5) >> endobj 120 0 obj (1.10.5 Proof of equality \(1.5.2\)) endobj 121 0 obj << /S /GoTo /D (subsection.1.10.6) >> endobj 124 0 obj (1.10.6 Proof of optimality criterion \(Proposition 1.7.2\)) endobj 125 0 obj << /S /GoTo /D (subsection.1.10.7) >> endobj 128 0 obj (1.10.7 Characterization of the value function as the maximum solution of BSDE \(1.3.3\)) endobj 129 0 obj << /S /GoTo /D (chapter.2) >> endobj 132 0 obj (2 Optimization under Full/Partial Information) endobj 133 0 obj << /S /GoTo /D (section.2.1) >> endobj 136 0 obj (2.1 Introduction) endobj 137 0 obj << /S /GoTo /D (section.2.2) >> endobj 140 0 obj (2.2 The model) endobj 141 0 obj << /S /GoTo /D (section.2.3) >> endobj 144 0 obj (2.3 Logarithmic utility function) endobj 145 0 obj << /S /GoTo /D (section.2.4) >> endobj 148 0 obj (2.4 Power utility) endobj 149 0 obj << /S /GoTo /D (subsection.2.4.1) >> endobj 152 0 obj (2.4.1 Optimization over bounded strategies) endobj 153 0 obj << /S /GoTo /D (subsection.2.4.2) >> endobj 156 0 obj (2.4.2 General case) endobj 157 0 obj << /S /GoTo /D (subsection.2.4.3) >> endobj 160 0 obj (2.4.3 Several default times and several assets) endobj 161 0 obj << /S /GoTo /D (section.2.5) >> endobj 164 0 obj (2.5 The partial information case) endobj 165 0 obj << /S /GoTo /D (subsection.2.5.1) >> endobj 168 0 obj (2.5.1 Filtering) endobj 169 0 obj << /S /GoTo /D (subsection.2.5.2) >> endobj 172 0 obj (2.5.2 Optimization problem for the logarithmic and power utility functions) endobj 173 0 obj << /S /GoTo /D (subsection.2.5.3) >> endobj 176 0 obj (2.5.3 Optimization problem for the exponential utility function and indifference pricing) endobj 177 0 obj << /S /GoTo /D (section.2.6) >> endobj 180 0 obj (2.6 Appendix) endobj 181 0 obj << /S /GoTo /D (subsection.2.6.1) >> endobj 184 0 obj (2.6.1 Proof of Propositions 2.4.2 and 2.4.3) endobj 185 0 obj << /S /GoTo /D (subsection.2.6.2) >> endobj 188 0 obj (2.6.2 Proof of Theorem 2.4.1) endobj 189 0 obj << /S /GoTo /D (subsection.2.6.3) >> endobj 192 0 obj (2.6.3 Proof of Theorem 2.4.2) endobj 193 0 obj << /S /GoTo /D (subsection.2.6.4) >> endobj 196 0 obj (2.6.4 Proof of Lemma 2.5.3) endobj 197 0 obj << /S /GoTo /D (part.2) >> endobj 200 0 obj (II PROGRESSIVE ENLARGEMENT OF FILTRATIONS AND BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS) endobj 201 0 obj << /S /GoTo /D (chapter.3) >> endobj 204 0 obj (3 BSDEs with jumps) endobj 205 0 obj << /S /GoTo /D (section.3.1) >> endobj 208 0 obj (3.1 Introduction) endobj 209 0 obj << /S /GoTo /D (section.3.2) >> endobj 212 0 obj (3.2 Progressive enlargement of filtrations) endobj 213 0 obj << /S /GoTo /D (section.3.3) >> endobj 216 0 obj (3.3 Decomposition of BSDEs with jumps) endobj 217 0 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endobj 292 0 obj (4.4.3 Comparison on scenarios) endobj 293 0 obj << /S /GoTo /D (section.4.5) >> endobj 296 0 obj (4.5 Appendix) endobj 297 0 obj << /S /GoTo /D (subsection.4.5.1) >> endobj 300 0 obj (4.5.1 Proofs of Lemmas 4.2.1 and 4.2.2) endobj 301 0 obj << /S /GoTo /D (AMS.102) >> endobj 304 0 obj (Bibliography) endobj 305 0 obj << /S /GoTo /D [306 0 R /Fit ] >> endobj 308 0 obj << /Length 1256 /Filter /FlateDecode >> stream xڭVr6}W-Lw0orڊmIi.DPË[ @Qy'bq&̙0Obj}9ƣ@ȄCZYrlGiDjr&$H(և$UV1T}K(CmZeJ'(c "r#EB9$B/n?Nc)ǵM]gԞK'