Finance 2: Dynamic Portfolio Choice (Fin2)

Competencies

1. Formulate and analyze decision problems (investment/consumption and optimal stopping) in a stochastic multi-period setting.
2. Analyze model consequences “with numbers”; algorithmically, experimentally or empirically. (As well as understand why these three things are different concepts.)
3. Acquire the confidence to read presentations of the same – or almost the same – problem in the literature. Know that notation, motivation, and rigour varies and that there is rarely a gospel.   

Skills

• Rigorously prove optimality principles and conditions for stochastic control problems in (discrete time, finite space)-multi-period setting.
• Explicitly solve simple investment/consumption and optimal stopping problems.   
• Derive (with pen and paper), analyze (with a computer) and explain (in plain English) model implications; be they quantitative or qualitative, be they regarding policy, equilibrium, or empirics.

Knowledge

• A closer look at arbitrages: No arbitrage-intervals in incomplete markets, cross-currency betting arbitrage, statistical arbitrage.
• Maximization of expected utility and (partial) equilibrium in one-period models, the state-price utility theorem and betting against beta.
• Multi-period optimal portfolio choice. The martingale method vs. dynamic programming/the Bellman equation.
• Explicit solutions in binomial(‘ish) models and in amodel with reurn preditability and transaction costs. 
• Properties and consequences of solutions; myopia and constant weights, C-CAPM, the equity premium puzzle.
• The numeraire porttfolio.
• Optimal stopping and the hedging and pricing of American options including Longstaff and Schwartz' simulation technique.