Computational Finance

The optimal control and hedging of portfolios of physical assets are also gaining importance due to the advancing decentralization of power generation. Suppose one wants to take future price uncertainties into account during optimization. In that case, the solution of the problem often becomes computationally intensive. Additionally, it requires experienced developers who can make necessary adjustments to the parameterization of the algorithm when the portfolio composition changes. To develop a generic framework for describing and solving such tasks, the business area uses methods from the field of reinforcement learning. This term refers to machine learning methods in which a software agent learns strategies that help to solve a complex optimization problem. With the help of such methods, companies can optimally manage their portfolios in a cost-saving and straightforward way.

Artificial intelligence (AI) models, especially in deep learning, are often "black boxes" for users. It is hardly understandable how these models come to important decisions. In the field of Explainable Artificial Intelligence (XAI), the business area is developing methods that help explain decisions made by AI models. One example is determining the influence of individual input data on the result at a selected data point. Another approach is to describe complicated models by simpler ones, making it easier to understand decisions. If, for example, an algorithm must decide whether a loan is granted, such a procedure can clarify in individual cases which factors are decisive for the decision. This is essential for a justification to customers and superiors and regarding applicable regulations. Furthermore, such approaches help improve AI models and detect bias in data.

Uncertainty occurs in all areas of the financial market, concerning valuation and risk models as well as market parameters. One of these market parameters is the bid-ask spread, which describes the difference between buying and selling offers. But how do you deal with uncertainties in your models? And what influence does uncertainty have on the price of derivatives? In essence, derivatives are contracts between two parties which stipulate that an underlying asset, such as a share or commodity, can be bought at a certain point in time for a price specified in advance.

The business area develops efficient algorithms and risk measures to answer these questions. In the procedures for measuring uncertainty, computationally intensive valuation and risk models have to be evaluated. Highly efficient algorithms, as well as modern multilevel approaches, are used here.

For several years now, cryptocurrencies and smart contracts have become more relevant in financial mathematics. Technically, smart contracts are programs stored in a blockchain that map the logic of contractual arrangements. They are executed when certain conditions are met. The business area develops procedures for analyzing blockchains. These procedures are based on graph algorithms and use machine learning methods. They can be applied for various purposes here, for example to analyze the trading behavior of market participants. Since cryptocurrencies such as Bitcoin or Ether offer a space for criminal activities due to their anonymity, an important aspect is detecting and analyzing activities such as money laundering or the theft of coins.

Computational Finance is an exciting interdisciplinary subfield of Scientific Computing, offering numerous topics for theses or internships. We look forward to hearing from you.