Taught in Lent Term by the Faculty of Mathematics (part of the Maths Part III degree).
This course studies a wide range of optimal investment/consumption problems that arise in theory and practice, and discusses the usefulness of the conclusions. Most examples studied will be in a continuous-time setting.
The following provisional list of topics indicates some of the intended content:
Self-financing portfolios and the wealth equation The Merton problem and its solution in the CRRA case, using the Hamilton-Jacobi-Bellman approach The Merton problem, general case, by martingale representation The Merton problem, general case, using state-price density approach (Davis-Varaiya) martingale principle of optimal control Dual methodology and the Pontryagin principle Equilibrium pricing The equity premium puzzle Utility-indifference pricing Lagrangian martingale characterisation of optimal solutions Imperfections: transaction costs, portfolio constraints, parameter uncertainty, infrequent rebalancing Varied objectives: ratcheting of consumption, habit formation, recursive utility Backward SDEs and optimal control How good are any of these rules in practice? A firm grasp of martingale theory, and a working knowledge of (Brownian) stochastic calculus will be required in the course.
Assessed by examination.
Course Leader Professor Chris Rogers » Faculty of Mathematics
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发表于 2013-2-28 09:23:02
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