| | Preface |
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| 1 | Stochastic Control in Discrete Time |
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| 1.1 | Dynamic Programming |
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| 1.1.1 | Introduction |
| 1.1.2 | Dynamic Programming |
| 1.1.3 | The Optimal Strategy |
| 1.1.4 | Numerical Solutions for T = ∞ |
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| 1.2 | Optimal Dividend Strategies in Risk Theory |
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| 1.2.1 | The Model |
| 1.2.2 | The Optimal Strategy |
| 1.2.3 | Premia of Size One |
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| 1.3 | Minimising Ruin Probabilities |
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| 1.3.1 | Optimal Reinsurance |
| 1.3.2 | Optimal Investment |
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| 2 | Stochastic Control in Continuous Time |
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| 2.1 | The Hamilton Jacobi Bellman Approach |
| 2.2 | Minimising Ruin Probabilities for a Diffusion Approximation |
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| 2.2.1 | Optimal Reinsurance |
| 2.2.2 | Optimal Investment |
| 2.2.3 | Optimal Investment and Reinsurance |
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| 2.3 | Minimising Ruin Probabilities for a Classical Risk Model |
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| 2.3.1 | Optimal Reinsurance |
| 2.3.2 | Optimal Investment |
| 2.3.3 | Optimal Reinsurance and Investment |
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| 2.4 | Optimal Dividends in the Classical Risk Model |
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| 2.4.1 | Restricted Dividend Payments |
| 2.4.2 | Unrestricted Dividend Payments |
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| 2.5 | Optimal Dividends for a Diffusion Approximation |
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| 2.5.1 | Restricted Dividend Payments |
| 2.5.2 | Unrestricted Dividend Payments |
| 2.5.3 | A Note on Viscosity Solutions |
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| 3 | Problems in Life Insurance |
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| 3.1 | Merton's Problem for Life Insurers |
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| 3.1.1 | The Classical Merton Problem |
| 3.1.2 | Single Life Insurance Contract |
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| 3.2 | Optimal Dividends and Bonus Payments |
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| 3.2.1 | Utility Maximisation of Dividends |
| 3.2.2 | Utility Maximisation of Bonus |
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| 3.3 | Optimal Control of a Pension Fund |
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| 3.3.1 | No Constraints |
| 3.3.2 | Fixed θ |
| 3.3.3 | Fixed c |
| 3.3.4 | Power Loss Function and σB = 0 |
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| 4 | Asymptotics of Controlled Risk Processes |
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| 4.1 | Maximising the Adjustment Coefficient |
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| 4.1.1 | Optimal Reinsurance |
| 4.1.2 | Optimal Investment |
| 4.1.3 | Optimal Reinsurance and Investment |
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| 4.2 | Cramér-Lundberg Approximations for Controlled Classical Risk Models |
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| 4.2.1 | Optimal Proportional Reinsurance |
| 4.2.2 | Optimal Excess of Loss Reinsurance |
| 4.2.3 | Optimal Investment |
| 4.2.4 | Optimal Proportional Reinsurance and Investment |
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| 4.3 | The Heavy-Tailed Case |
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| 4.3.1 | Proportional Reinsurance |
| 4.3.2 | Excess of Loss Reinsurance |
| 4.3.3 | Optimal Investment |
| 4.3.4 | Optimal Proportional Reinsurance and Investment |
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| A | Stochastic Processes and Martingales |
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| A.1 | Stochastic Processes |
| A.2 | Filtration and Stopping Times |
| A.3 | Martingales |
| A.4 | Poisson Processes |
| A.5 | Brownian Motion |
| A.6 | Stochastic Integrals and Itô's Formula |
| A.7 | Some Tail Asymptotics |
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| B | Markov Processes and Generators |
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| B.1 | Definition of Markov Processes |
| B.2 | The Generator |
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| C | Change of Measure Techniques |
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| C.1 | Introduction |
| C.2 | The Brownian Motion |
| C.3 | The Classical Risk Model |
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| D | Risk Theory |
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| D.1 | The Classical Risk Model |
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| D.1.1 | Introduction |
| D.1.2 | Small Claims |
| D.1.3 | Large Claims |
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| D.2 | Perturbed Risk Models |
| D.3 | Diffusion Approximations |
| D.4 | Premium Calculation Principles |
| D.5 | Reinsurance |
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| E | The Black Scholes Model |
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| F | Life Insurance |
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| F.1 | Classical Life Insurance |
| F.2 | Bonus Schemes |
| F.3 | Unit-Linked Insurance Contracts |
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| | References |
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| | List of Principal Notation |
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| | Index |
