Asset liability management (ALM) attempts to find the optimal investment strategy under uncertainty in both asset and liability streams. In order to deal with the stochastic nature of assets, interest rates and liabilities and furthermore, with the dynamic nature of investing, complex optimization problems have to be solved. The essential mathematical tools of modern portfolio construction methods are stochastic control and stochastic programming. The course will cover the following topics: in the first part, some classical financial optimization models are reviewed, measures of dispersion, measures of risk, probabilities metrics are defined and simple optimization problems are solved. The second part of the course will be an introduction to stochastic programming, single and multistage optimization, scenario generation, dynamic portfolio optimization with stochastic programming. Empirical distributions for stock prices and returns have found that the extreme values are more likely than would be predicted by the normal distribution. This is the reason why in the third part, the more general and adequate alpha stable distribution is introduced. Some general notions about ideal probabilities metrics, copula functions, and performance measures will be given during the course. Practical examples and exercises will help to better understand empirical applications of ALM techniques.
S. A. Zenios. Financial Optimization, Cambridge University Press, 1993.
S. A. Zenios. Practical Financial Optimization: Decision Making for Financial Engineers, John Wiley, 2008.
M. Uhrig-Homburg. Fremdkapitalkosten, Bonitätsrisiken und optimale Kapitalstruktur, Beiträge zur betriebswirtschaftlichen Forschung 92, Gabler Verlag, 2001
S.T. Rachev, Ch. Menn and F.J. Fabozzi. Fat-Tailed and Skewed Asset Return Distributions: Implications for Risk Management, Portfolio selection, and Option Pricing. John Wiley, Finance, 2005.
F.J Fabozzi and A. Konishi. The Handbook of Asset/Liability Management: State-of-Art Investment Strategies, Risk Controls and Regulatory Required. Wiley, 1995.B. Scherer and R.D. Martin. Introduction to Modern Portfolio Optimization with NuOPT, S-PLUS and S+Bayes. Springer, 2005.