Financial and Actuarial Mathematics
TU Wien, Austria

2011-01-25  PDF  MS-Word

## Prof. Dr. Nicole Bäuerle

Institut für Stochastik, Karlsruher Institut für Technologie (KIT)
http://www.mathematik.uni-karlsruhe.de/stoch/~baeuerle/de

## The Relaxed Investor with Partial Information

We consider an investor in a financial market consisting of a riskless bond and several risky assets. The price processes of the risky assets are geometric Brownian motions where either the drifts are modelled as random variables assuming a constant volatility matrix or the volatility matrix is considered random and drifts are assumed to be constant. The investor is only able to observe the asset prices but not all the model parameters and hence information is only partial. A Bayesian approach is used with known prior distributions for the random model parameters. We assume that the investor can only trade at discrete time points which are multiples of h>0 and investigate the loss in expected utility of terminal wealth which is due to the fact that the investor cannot trade and observe continuously. It turns out that in general a discretization gap appears, i.e for h\to 0 the expected utility of the h-investor does not converge to the expected utility of the continuous investor. This is in contrast to results under full information in (Rogers, L.C.G. 2001. The relaxed investor and parameter uncertainty. Finance and Stochastics, 5(2), 131-154). We also present simple asymptotically optimal portfolio strategies for the discrete-time problem. Our results are illustrated by some numerical examples.
The talk is based on joint work with S. Urban and L. Veraart.

Zur Person: Nicole Bäuerle is full professor for Stochastics at the Karlsruhe Institute of Technology. Currently she is in the board of the Fachgruppe Stochastik and the DGVFM (Deutsche Gesellschaft für Versicherungs- und Finanzmathematik). Her research areas include applied probability, stochastic processes and control as well as financial and actuarial mathematics. She is editor of the journals "Stochastic Models" and "Mathematical Methods of Operations Research".

 Termin: Dienstag, 25. Jänner 2011, 16:45 Uhr s.t. Ort: Technische Universität Wien 1040 Wien, Wiedner Hauptstraße 8-10 Freihaus, Turm B (gelber Bereich), 2. Stock, Hörsaal FH 3

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Mag. Christoph Krischanitz
Präsident der Aktuarvereinigung Österreichs
Präsident des Österreichischen Förderungsvereins der Versicherungsmathematik

Dr. Franz Kronsteiner
Präsident der Österreichische Gesellschaft für Versicherungsfachwissen

o.Univ.-Prof. Dr. Walter Schachermayer
Fakultät für Mathematik, Universität Wien

Univ.-Prof. Dr. Uwe Schmock
Finanz- und Versicherungsmathematik (FAM), Technische Universität Wien