Optimal Portfolios: Stochastic Models for Optimal Investment and Risk Management in Continuous Time Book

	Preface
	Some Guidelines and General Notations
Ch. 1	Introduction and Discrete-Time Models	1
1.1	General and Historic Remarks: A Short Survey	1
1.2	Mean-Variance Analysis in a One-Period Model: The Markowitz-Approach	4
1.3	More on One-Period and Discrete-Time Approaches to Portfolio Selection	11
1.4	Criticisms and Limitations of Discrete-Time Models	12
Ch. 2	The Continuous-Time Market Model	15
2.1	The Security Price Processes	15
2.2	The Wealth Process and the Actions of a Small Investor	21
2.3	Completeness of the Market Model and the Growth-Optimum Portfolio	25
2.4	Option Pricing: A Short Introduction	29
2.5	Convergence of Discrete Markets to Continuous Markets	34
Ch. 3	The Continuous-Time Portfolio Problem	37
3.1	Introduction and Formulation of the Problem	37
3.2	Comparison between Stochastic Control and Martingale Method - A Preview via a Simple Discrete Example	41
3.3	The Stochastic Control Method to Solve the Portfolio Problem	48
3.4	The Martingale Approach to the Continuous-Time Portfolio Problem	59
3.5	The Martingale Method Revisited ae Pliska's Version	82
3.6	An Application: "Minimising the Difference to the Terminal Wealth of a Richer Investor?"	92
Ch. 4	Constrained Continuous-Time Problems	101
4.1	Portfolio Problems with Constraints	101
4.2	A Dual Method to Solve Portfolio Problems with Constraints on the Terminal Wealth	101
4.3	A Continuous-Time Mean-Variance Problem	111
4.4	Portfolio Problems with Constrained Strategies	118
4.5	Some Examples of Constrained Problems	143
Ch. 5	Portfolio Optimisation in the Presence of Transaction Costs	151
5.1	Optimal Life-Time Consumption with Proportional Transaction Cots	151
5.2	Impulse Control Methods and Portfolio Optimisation with Strictly Positive Transaction Costs	171
5.3	Maximising the Growth Rate Under Fixed Transaction Costs	206
Ch. 6	Non-Utility Based Portfolio Selection Models	223
6.1	Universal Portfolios: The Discrete-Time Model	223
6.2	Asymptotically Optimal Portfolios and Universal Portfolios in Continuous Time	240
6.3	Optimal Cash Management in Equity Index Tracking with Transaction Costs	259
6.4	Value Preserving Portfolio Strategies	279
	Appendix	295
A	Normal Distribution, Conditional Expectation, Stochastic Processes	295
B	Introduction to Stochastic Integrals and the Ito-Calculus	303
C	Controlled Stochastic Differential Equations	320
D	Laplace's Method of Integration	328
E	Optimisation of Convex Functionals	328
	References	331
	Index	337