Research

Online Conversion Problems

Decisions when to convert an asset can be supported by the use of online algorithms. Before an algorithm is applied one should be interested in its performance. Our focus is to analyze the performance of online trading algorithms by two different approaches. The first is assuming uncertainly about asset prices and analyzing algorithms assuming worst-case competitive analysis. The second one is a heuristic approach where algorithms are implemented and the analysis is done on historic data by simulation runs. We apply the second approach and compare the results to these of the first one. We consider different conversion problems, and analyze online algorithms from a worst-case and an empirical-case point of view. For references see:

  •  Mohr, E.; Schmidt, G.: How much is it worth to know the furure in online conversion problems?, Discrete Applied Mathematics 161, pp. 1546-1555, 2013
  • Schmidt, G.; Mohr, E.; Kersch, M.: Experimental Analysis of an Online Trading Algorithm, Electronic Notes in Discrete Mathematics 36, 519-526, 2010

 

Online Portfolio Selection Problems

The objective of online portfolio selection is to design provably good algorithms with respect to some on-line or offline benchmark. Online portfolio selection is a fundamental problem in computational finance, which has been extensively studied across several research communities, including finance, statistics, artificial intelligence, machine learning and data mining, etc.

Portfolio Selection aims to optimize the allocation of wealth across a set of assets. It is a fundamental research problem in computational finance and a practical engineering task in financial engineering. On-line portfolio selection, which sequentially selects a portfolio over a set of assets in order to achieve certain targets, is a natural and important task for asset management community. For references see:

  • Dochow R., Mohr E., Schmidt G.: Risk-Adjusted On-line Portfolio Selection, in: Operations Research Proceedings 2013, 113-119, Springer 2014

 

Personal Financial Planning

This research field tackles questions regarding the ongoing computer-assisted process of defining personal financial goals, alternative ways to meet these goals and how to realize that way that best suits one's life circumstances. Decisions regarding the optimal usage of financial means under financial and personal restrictions are at the very core of personal financial planning. With personal financial planning associated research fields are tax planning, pension planning, portfolio selection, liquidity planning, wealth management , risk management and so on. 

  • Schmidt, G.: Persönliche Finanzplanung, 3. Auflage, Springer, 2016