This course starts with the foundations of optimal portfolio theory
from Markowitz's mean-variance analysis to modern utility theory. We
will present the solution to Merton's problem for different types of
utility functions in both discrete and continuous time models, using
the techniques of stochastic control and convex duality. We then move
to the subject of rational pricing mechanisms in incomplete markets,
concluding
with a review of several concrete examples of utility
indifference prices.
References
- Markowitz, H.
Portfolio Selection, The Journal
of Finance,
VII (1), 77-91,
1952.
- Sharpe, W.
Capital
Asset Prices: a theory of market equilibrium under conditions of risk, The
Journal of Finance,
XIX (3),
425-441, 1964.
- Fama, E.
Efficient Capital Markets: a review of
theory amd empirical work, The Journal of Finance,
XXV (2), 383-417, 1970.
- Arrow, K. and Debreu,
G.
Existence of an Equilibrium
for a Competitive Economy, Econometrica,
22 (3), 265-290, 1954.
- Schachermayer, W.
Portfolio Optimization in Incomplete
Financial Markets. Notes of the Scuola Normale Superiore
Cattedra Galileiana, Pisa, 2004.
- Schachermayer, W.
Portfolio Optimization in Incomplete
Financial Markets. Notes of the Scuola Normale Superiore
Cattedra Galileiana, Pisa, 2004.
- Harrison, J. M and Pliska, S.
R.
A Stochastic Calculus Model of
Continuous Trading: Complete Markets, Stoch. Proc. and Appl,
15, 313--316, 1983.
- Zariphopoulou, T.
Stochastic Control Methods in Asset Pricing,
in Handbook of Stochastic Analysis and Applications, Kanna, D. (ed),
Marcel Deker, 2001.
- Karatzas, I., Lehocsky, J, Shreve, S.
and Xu, G.
Martingale and Duality
Methods for Utility Maximization in an Incomplete Market, SIAM
J. Control and Optimization,
29 (3),
703--730, 1991.
- Karatzas, I., Lehocsky, J, Shreve,
S.
and Xu, G.
Martingale and Duality
Methods for Utility Maximization in an Incomplete Market, SIAM
J. Control and Optimization,
29 (3),
703--730, 1991.
- Musiela, M and Zariphopoulou, T.
A valuation algortihm for indifference
prices in incomplete markets, Finance and Stochastics,
8, 399-414, 2004.
- Musiela, M and Zariphopoulou,
T.
A valuation algortihm for
indifference prices in incomplete markets, Finance and
Stochastics,
8, 399-414, 2004.
Assignments