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November 06, 2009
I am a fourth-year doctoral student at the Department of Statistics at Columbia. Before I came here I did a Masters' at Texas A&M (in 2005, Math Finance) and a German 'Diplom' at the University of Ulm (in 2006, 'Wirtschaftsmathematik'). I like to use mathematical concepts in real-world situations, especially applying probabilistic ideas in financial and economical contexts. My advisor is Ioannis Karatzas.
I grew up in a large family, together with four younger brothers and, for several years, a foster sister. After graduating from highschool I did my alternative service at the emergency service of my home town. That year was rich of valuable experiences and I kept volunteering at the emergence service for several years after that. I am involved in the Leo Club, an international service club. I was president of my local club in 2003 and 2004. I enjoy reading, hanging out with friends, and doing sports. I have started to play Squash at Columbia.
As a mathematician and statistician I have a quantitative background. I see my research as two-sided. On one side, I like working on probabilistic and statistical problems. On the other side, I enjoy doing interdisciplinary research. I feel that a joint work obtains new perspectives which are more valuable than the sum of the single perpectives. Also, working with researchers from other fields expands my personal horizone. So far, I have mainly worked in three fields: stochastic portfolio theory, credit risk and economic learning theory.
Stochastic portfolio theory is a descriptive theory, which provides a framework to analyze portfolios, stock market structures and arbitrage opportunities. It has been pioneered by Robert Fernholz, Ioannis Karatzas and co-authors. In my work, I show how optimal portfolios can be computed within this framework, which generalizes the usual analysis of bubbles. It is shown that standard delta hedging is optimal and a modified put-call parity for models with arbitrage is derived. From a mathematical point of view, there exists not necessariliy an equivalent local martingale measure. The Föllmer measure is used to simplify computations.
Working paper: Optimal trading strategies under arbitrage (April 2009)
Credit risk: The market of credit derivatives has grown rapidly over the last decade. Efficient pricing routines in realistic (and thus, most times sophisticated) models are crucial for the financial industry. Recent literature distinguishes between structural and intensity-based models. In our research, we focus on structural models. These models link the notation of default to an economic interpretation. The default of a company is modelled by the first time when the firm-value process crosses a 'default barrier'. Allowing jumps in the firm-value process leads to realistic short-term spreads. However, in most cases it comes at the cost of analytical tractability. In our work we develop and compare pricing algorithms for corporate bonds, the fundamental products on the credit market.
Working paper: Pricing corporate bonds in an arbitrary jump-diffusion model based on an improved Brownian-bridge algorithm
(November 2009, joint work with Matthias Scherer)
Diplom thesis: Structural Default Models with Jumps (June 2006, awarded DZ-Bank Karrierepreis 2007)
Economic learning theory: In setups where the payoff distributions are unknown and decision makers are not assumed to form beliefs, expected utility theory cannot be applied. One way out of this is the introduction of the notion of a behavioral rule, which represents the probability of playing each action. We analyze a model where individuals have little information about the payoff distributions associated with the actions they play. In every period they observe the payoffs of their own action and of the played action of another agent. We characterize the behavioral rules in this setup in terms of different criteria regarding their performance.
Paper: Monotone imitation, Economic Theory, 2009, Volume 41, Issue 3 (June 2008, joint work with Carlos Oyarzun. The original publication is available at www.springerlink.com.)
Other topics: Social networks have been in the focus of researchers for a long time. In the last years, more and more data become available, which require statistical modeling. In this work, we explore the influence of social structure on opinions about contemporary political issues.
Working paper: Comparing two methods for predicting opinions using social structure (September 2009, joint work with Tyler McCormick, Amal Moussa, Thomas DiPrete, Andrew Gelman, Julien Teitler, Tian Zheng)
B-splines of third order are a special representation of cubic splines and are written as weighted sum of twice differentiable basis functions consisting of four segments. They are defined via a recursive convolution formula. We present here the analytical formulas for the basis functions and list the interpolation equations for the weights in the case of natural boundary conditions. These formulas can be derived from easy computations and are well-known. However, we have not found them explicitly written out in the literature.
Working paper: B-splines of third order on a non-uniform grid (August 2008)
During several internships I had great opportunites not only facing exciting challenges but also participating in the transformation of theoretical knowledge into valuable products.
- J.P. Morgan, Investment banking division, Quantitative research, Equities (2008)
- d-fine GmbH, Consulting in quantitative and technical risk management (2006)
- Commerzbank, Investment banking division, Quantitative research, FX (2004)
- Rohde & Schwarz (1998, 1999)
E-Mail: ruf (at) stat (dot) columbia.edu
Skype, MSN, ICQ, Xing: on request