| Preface | p. VII |
| Stochastic Control in Discrete Time | p. 1 |
| Dynamic Programming | p. 1 |
| Introduction | p. 1 |
| Dynamic Programming | p. 2 |
| The Optimal Strategy | p. 4 |
| Numerical Solutions for T = [infinity] | p. 6 |
| Optimal Dividend Strategies in Risk Theory | p. 9 |
| The Model | p. 9 |
| The Optimal Strategy | p. 12 |
| Premia of Size One | p. 16 |
| Minimising Ruin Probabilities | p. 20 |
| Optimal Reinsurance | p. 20 |
| Optimal Investment | p. 24 |
| Stochastic Control in Continuous Time | p. 27 |
| The Hamilton-Jacobi-Bellman Approach | p. 28 |
| Minimising Ruin Probabilities for a Diffusion Approximation | p. 34 |
| Optimal Reinsurance | p. 34 |
| Optimal Investment | p. 39 |
| Optimal Investment and Reinsurance | p. 42 |
| Minimising Ruin Probabilities for a Classical Risk Model | p. 43 |
| Optimal Reinsurance | p. 44 |
| Optimal Investment | p. 54 |
| Optimal Reinsurance and Investment | p. 64 |
| Optimal Dividends in the Classical Risk Model | p. 69 |
| Restricted Dividend Payments | p. 70 |
| Unrestricted Dividend Payments | p. 79 |
| Optimal Dividends for a Diffusion Approximation | p. 97 |
| Restricted Dividend Payments | p. 97 |
| Unrestricted Dividend Payments | p. 102 |
| A Note on Viscosity Solutions | p. 104 |
| Problems in Life Insurance | p. 113 |
| Merton's Problem for Life Insurers | p. 114 |
| The Classical Merton Problem | p. 114 |
| Single Life Insurance Contract | p. 122 |
| Optimal Dividends and Bonus Payments | p. 127 |
| Utility Maximisation of Dividends | p. 127 |
| Utility Maximisation of Bonus | p. 132 |
| Optimal Control of a Pension Fund | p. 135 |
| No Constraints | p. 136 |
| Fixed [theta] | p. 141 |
| Fixed c | p. 142 |
| Power Loss Function and [sigma subscript B] = 0 | p. 143 |
| Asymptotics of Controlled Risk Processes | p. 147 |
| Maximising the Adjustment Coefficient | p. 147 |
| Optimal Reinsurance | p. 148 |
| Optimal Investment | p. 152 |
| Optimal Reinsurance and Investment | p. 153 |
| Cramer-Lundberg Approximations for Controlled Classical Risk Models | p. 154 |
| Optimal Proportional Reinsurance | p. 154 |
| Optimal Excess of Loss Reinsurance | p. 163 |
| Optimal Investment | p. 165 |
| Optimal Proportional Reinsurance and Investment | p. 171 |
| The Heavy-Tailed Case | p. 174 |
| Proportional Reinsurance | p. 174 |
| Excess of Loss Reinsurance | p. 179 |
| Optimal Investment | p. 181 |
| Optimal Proportional Reinsurance and Investment | p. 194 |
| Stochastic Processes and Martingales | p. 201 |
| Stochastic Processes | p. 201 |
| Filtration and Stopping Times | p. 201 |
| Martingales | p. 202 |
| Poisson Processes | p. 203 |
| Brownian Motion | p. 205 |
| Stochastic Integrals and Ito's Formula | p. 206 |
| Some Tail Asymptotics | p. 209 |
| Markov Processes and Generators | p. 211 |
| Definition of Markov Processes | p. 211 |
| The Generator | p. 211 |
| Change of Measure Techniques | p. 215 |
| Introduction | p. 215 |
| The Brownian Motion | p. 216 |
| The Classical Risk Model | p. 217 |
| Risk Theory | p. 219 |
| The Classical Risk Model | p. 220 |
| Introduction | p. 220 |
| Small Claims | p. 221 |
| Large Claims | p. 223 |
| Perturbed Risk Models | p. 225 |
| Diffusion Approximations | p. 226 |
| Premium Calculation Principles | p. 227 |
| Reinsurance | p. 228 |
| The Black-Scholes Model | p. 231 |
| Life Insurance | p. 235 |
| Classical Life Insurance | p. 235 |
| Bonus Schemes | p. 237 |
| Unit-Linked Insurance Contracts | p. 238 |
| References | p. 241 |
| List of Principal Notation | p. 251 |
| Index | p. 253 |
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