In this talk we examine analytical properties of drawdowns as path dependent measures of risk. To this effect we derive analytical formulas of the joint law of drawdowns and the speed with which they are realized. We also examine the problem of valuation of drawdown insurance in the form of digital contracts based on drawdown events. We demonstrate that it is possible to replicate the payoff of such contracts by actual trade instruments. We also consider the problem of valuation of such insurance contracts through a continuously paid risk premium and the optimal termination strategy of such a contract under appropriate conditions.
Olympia Hadjiliadis was born in Athens Greece. All of her undergraduate studies were completed in Toronto, Canada, where she studied Statistics. She then completed a Master's degree in Mathematics with specialization in Statistics and Finance at the University of Waterloo in Waterloo, Canada. Ms. Hadjiliadis worked as an intern for Citibank Canada and as an Associate Financial Engineer at Algorithmics Inc. in Toronto, Canada. She then completed her PhD at the Department of Statistics of Columbia University in 2005 with distinction under the supervision of JanVecer and the mentorship of G.V. Moustakides. Ms. Hadjiliadis finally joined the group of Dean H. V. Poor as a postdoc at Princeton's Department of Electrical Engineering for two years before assuming her position at the City University of New York. Her research interests began in the area of quickest detection and sequential analysis. In her earlier years as a researcher I have addressed fundamental problems arising in the area of quickest detection and sequential analysis. For this work she received the NSA Young Investigator's award by the Division of Mathematical and Physical Science in the area of Probability in 2009. Since then, in her attempt to seek further applications of quickest detection and statistical surveillance, she became involved in the development of algorithms for online detection and classification of objects in point clouds of urban scenes, a problem in computer vision. This work has led to further external funding by the NSF. She has also been involved in the area of financial engineering through the study of drawdowns and drawdown insurance and more recently in the applications of detection algorithms in algorithmic trading.