Einladung zur Vortragsreihe aus Finanz- und Versicherungsmathematik

Dr. Carole Bernard

Department of Statistics and Actuarial Science, University of Waterloo
http://sas.uwaterloo.ca/Faculty/Bernard.shtml

Optimal investment under state-dependent constraints

Bernard and Boyle (2010) derive the lowest cost strategy (also called "cost-efficient" strategy) that achieves a given wealth distribution. An optimal strategy for a profit seeking investor with law-invariant preferences is then necessarily cost-efficient and is unique. In the specific case of a Black and Scholes market the optimal strategy is always path-independent. Assuming now that investors still want to achieve a given distribution at a fixed horizon but have additional state-dependent constraints, we propose an explicit construction of an optimal strategy. In the case of a Black and Scholes market, we show that it may now be path-dependent and that it is not unique.
This is joint work with Phelim Boyle (Wilfrid Laurier University) and Steven Vanduffel (Vrije Universiteit Brussels).

Zur Person: Professor Bernard received her PhD in 2005 from the Universite; Claude Bernard, Lyon. During her PhD studies she taught at ISFA, a graduate school of actuarial studies. From September 2006 to May 2007 she was a postdoctoral fellow at the University of Waterloo under the supervision of Professors Phelim Boyle, Mary Hardy, and Weidong Tian. In July 2007 she visited Professor Tahir Choulli at the University of Alberta.
During the past few years Professor Bernard has been working on some new applications of option theory in insurance. In particular, with co-authors Olivier Le Courtois and Francois Quittard-Pinon, both from Lyon, she provided a financial method to value certain participating life insurance policies (equity-indexed annuities) with a minimum guarantee taking into account both interest-rate risk and default risk. This study is in accordance with new accounting standards that require insurers to report their assets and liabilities at market values. Professor Bernard has also worked on the regulation and surveillance of financial institutions using exotic barrier options; for instance, Parisian options are used to model the existing regulations of the Italian insurance system for bank deposits.
Finally, Professor Bernard is interested in structured products. She has recently worked on the pricing of barrier options with her co-authors from Lyon. With Professor Phelim Boyle of Wilfrid Laurier University and Professor Weidong Tian, she has been working on the optimal design of structured products. They have provided a robust and optimal design, from the issuers perspective, of an investment contract that includes a minimum guarantee and the possibility (for the investor) to outperform a benchmark. This design completes the prior work of Professors P. Boyle and W. Tian on the design of such investments from the investors viewpoint.

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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