%PDF-1.5 % 1 0 obj << /S /GoTo /D (title.0) >> endobj 4 0 obj (Titlepage) endobj 5 0 obj << /S /GoTo /D (abstract.0) >> endobj 8 0 obj (Abstract) endobj 9 0 obj << /S /GoTo /D (acknowledgements.0) >> endobj 12 0 obj (Acknowledgements) endobj 13 0 obj << /S /GoTo /D (section*.4) >> endobj 16 0 obj (contents) endobj 17 0 obj << /S /GoTo /D (chapter.1) >> endobj 20 0 obj (1 Introduction) endobj 21 0 obj << /S /GoTo /D (section.1.1) >> endobj 24 0 obj (1.1 Introduction and Literature Review) endobj 25 0 obj << /S /GoTo /D (subsection.1.1.1) >> endobj 28 0 obj (1.1.1 Ruin Probability) endobj 29 0 obj << /S /GoTo /D (subsection.1.1.2) >> endobj 32 0 obj (1.1.2 Optimal investment Strategy and Gambling) endobj 33 0 obj << /S /GoTo /D (section.1.2) >> endobj 36 0 obj (1.2 Aims and objectives) endobj 37 0 obj << /S /GoTo /D (section.1.3) >> endobj 40 0 obj (1.3 Structure of the Thesis) endobj 41 0 obj << /S /GoTo /D (chapter.2) >> endobj 44 0 obj (2 The Ruin Probability with Brownian Motion) endobj 45 0 obj << /S /GoTo /D (section.2.1) >> endobj 48 0 obj (2.1 \040Introduction) endobj 49 0 obj << /S /GoTo /D (section.2.2) >> endobj 52 0 obj (2.2 The Model and Assumptions) endobj 53 0 obj << /S /GoTo /D (subsection.2.2.1) >> endobj 56 0 obj (2.2.1 Approaches to calculating n) endobj 57 0 obj << /S /GoTo /D (section.2.3) >> endobj 60 0 obj (2.3 First approach: Approximating the sum of correlated lognormal random variables) endobj 61 0 obj << /S /GoTo /D (section.2.4) >> endobj 64 0 obj (2.4 Second approach: Approximation by Brownian Motion) endobj 65 0 obj << /S /GoTo /D (section.2.5) >> endobj 68 0 obj (2.5 Integral of Exponential Brownian motion) endobj 69 0 obj << /S /GoTo /D (subsection.2.5.1) >> endobj 72 0 obj (2.5.1 \040The Law of At at fixed times ) endobj 73 0 obj << /S /GoTo /D (subsection.2.5.2) >> endobj 76 0 obj (2.5.2 Moments) endobj 77 0 obj << /S /GoTo /D (subsection.2.5.3) >> endobj 80 0 obj (2.5.3 Application) endobj 81 0 obj << /S /GoTo /D (subsection.2.5.4) >> endobj 84 0 obj (2.5.4 Numerical evaluation of the stochastic integral) endobj 85 0 obj << /S /GoTo /D (section.2.6) >> endobj 88 0 obj (2.6 Approximation of the Integral) endobj 89 0 obj << /S /GoTo /D (subsection.2.6.1) >> endobj 92 0 obj (2.6.1 First Approximation: Classical approach) endobj 93 0 obj << /S /GoTo /D (subsection.2.6.2) >> endobj 96 0 obj (2.6.2 Second Approximation: via Taylor Formula) endobj 97 0 obj << /S /GoTo /D (subsection.2.6.3) >> endobj 100 0 obj (2.6.3 Third Approximation: It\364 Formula) endobj 101 0 obj << /S /GoTo /D (section.2.7) >> endobj 104 0 obj (2.7 Simulation and Comparison) endobj 105 0 obj << /S /GoTo /D (subsection.2.7.1) >> endobj 108 0 obj (2.7.1 Basic Idea and Method) endobj 109 0 obj << /S /GoTo /D (subsection.2.7.2) >> endobj 112 0 obj (2.7.2 Comparison of mean and variance for different approximations ) endobj 113 0 obj << /S /GoTo /D (subsection.2.7.3) >> endobj 116 0 obj (2.7.3 Comparison of Simulated Ruin Probabilities) endobj 117 0 obj << /S /GoTo /D (section.2.8) >> endobj 120 0 obj (2.8 The Advanced Model) endobj 121 0 obj << /S /GoTo /D (subsection.2.8.1) >> endobj 124 0 obj (2.8.1 Construction of Model) endobj 125 0 obj << /S /GoTo /D (section.2.9) >> endobj 128 0 obj (2.9 Conclusion) endobj 129 0 obj << /S /GoTo /D (chapter.3) >> endobj 132 0 obj (3 Optimal constant fraction policies under the ruin probability constraints) endobj 133 0 obj << /S /GoTo /D (section.3.1) >> endobj 136 0 obj (3.1 Approach) endobj 137 0 obj << /S /GoTo /D (section.3.2) >> endobj 140 0 obj (3.2 The Construction of Model) endobj 141 0 obj << /S /GoTo /D (section.3.3) >> endobj 144 0 obj (3.3 Estimation: Likelihood Functions) endobj 145 0 obj << /S /GoTo /D (subsection.3.3.1) >> endobj 148 0 obj (3.3.1 Model 1) endobj 149 0 obj << /S /GoTo /D (subsection.3.3.2) >> endobj 152 0 obj (3.3.2 Model 2) endobj 153 0 obj << /S /GoTo /D (subsection.3.3.3) >> endobj 156 0 obj (3.3.3 \040Model 3-Binomial Model ) endobj 157 0 obj << /S /GoTo /D (subsection.3.3.4) >> endobj 160 0 obj (3.3.4 Model 4- Model with investment strategy with constant claim size) endobj 161 0 obj << /S /GoTo /D (subsection.3.3.5) >> endobj 164 0 obj (3.3.5 \040Model 5-Model with investment strategy with exponential claims) endobj 165 0 obj << /S /GoTo /D (subsection.3.3.6) >> endobj 168 0 obj (3.3.6 Model 6) endobj 169 0 obj << /S /GoTo /D (section.3.4) >> endobj 172 0 obj (3.4 Estimation of the parameters: Numerical Analysis with Stochastic Simulation) endobj 173 0 obj << /S /GoTo /D (subsection.3.4.1) >> endobj 176 0 obj (3.4.1 \040How to choose A0 in the simulation) endobj 177 0 obj << /S /GoTo /D (subsection.3.4.2) >> endobj 180 0 obj (3.4.2 The results of estimation) endobj 181 0 obj << /S /GoTo /D (subsection.3.4.3) >> endobj 184 0 obj (3.4.3 Discussion: Analysis of estimation) endobj 185 0 obj << /S /GoTo /D (section.3.5) >> endobj 188 0 obj (3.5 Optimal investment policy) endobj 189 0 obj << /S /GoTo /D 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(section.4.3) >> endobj 232 0 obj (4.3 The Simple Model with Heavy-Tailed Claims) endobj 233 0 obj << /S /GoTo /D (section.4.4) >> endobj 236 0 obj (4.4 Sum of Two Compound Poisson Processes ) endobj 237 0 obj << /S /GoTo /D (subsection.4.4.1) >> endobj 240 0 obj (4.4.1 Construction of new model) endobj 241 0 obj << /S /GoTo /D (subsection.4.4.2) >> endobj 244 0 obj (4.4.2 Model Expression) endobj 245 0 obj << /S /GoTo /D (subsection.4.4.3) >> endobj 248 0 obj (4.4.3 Moments of MGF) endobj 249 0 obj << /S /GoTo /D (section.4.5) >> endobj 252 0 obj (4.5 Conclusion) endobj 253 0 obj << /S /GoTo /D (chapter.5) >> endobj 256 0 obj (5 Concluding and further work) endobj 257 0 obj << /S /GoTo /D [258 0 R /FitH] >> endobj 260 0 obj << /Length 321 /Filter /FlateDecode >> stream xuRj0+ta5$ m(=T[e,%:CJbWhFGz|v0D1A9 g%z-*)r