Gerhard Larcher is an Austrian mathematician and professor of financial mathematics at the Johannes Kepler University (JKU) in Linz, Austria. [1] He is the head of the Institute of Financial Mathematics.
Gerhard Larcher studied mathematics at the University of Salzburg from 1978 to 1982 and received his doctorate with the highest distinction sub auspiciis Praesidentis under Harald Niederreiter in 1985; he completed his postdoc in mathematics four years later.
From 1983 to 2000, Larcher worked at the University of Salzburg as an assistant professor and lecturer and from 1996 as an associate professor of mathematics. During this time he headed the Institute of Mathematics for two years. Since 1999 he was speaker and leader of the FWF-Research Center (FSP) Number-Theoretic Algorithms and their Applications.
In 2000, Larcher was appointed as a full professor of financial mathematics at the Johannes Kepler University (JKU) in Linz, Austria. Three years later, he founded the asset management company Art In Finance in Vienna, which developed and implemented alternative investment strategies. After years of strong profits, the option strategies of Art In Finance sustained massive losses in the course of the financial crisis in 2008. [2] The strategies were then adapted accordingly and successfully reintroduced. At the start of 2017, he withdrew from the company and the asset management business. From 2003 to 2005, he was the department head of financial mathematics at the Johann Radon Institute for Computational and Applied Mathematics at the Austrian Academy of Sciences. [3]
Since 2014 he has been the speaker of the Austrian special research area Quasi-Monte Carlo Methods: Theory and Applications [4] at the Austrian Science Fund. [5] In addition to his work at the Johannes Kepler University, Larcher runs seminars and workshops in the field of quantitative finance.
He is the author of the monograph Quantitative Finance: Strategien, Investments, Analysen [6] published by Springer-Gabler Verlag, of the trilogy The Art of Quantitative Finance. Strategies, Investmens, Research by Springer and Die Black-Scholes-Theorie, In 100 Schritten vom Münzwurf zum Wirtschaftsnobelpreis [7] also published by Springer.
In 2019, he founded the Linz School of Quantitative Finance (LSQF), a work group at the JKU Linz that deals with finance consulting and the creation of highly specialized finance software. [8] Among other things, the LSQF team developed the Fynup Ratio, [9] a new method for measuring the quality of investment funds based on machine learning techniques.
His work and research focuses on the development and analysis of trading strategies, the valuation of derivative finance products, Monte Carlo and quasi-Monte Carlo methods and number theory. [10]
Johannes Kepler was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws of planetary motion, and his books Astronomia nova, Harmonice Mundi, and Epitome Astronomiae Copernicanae. These works also provided one of the foundations for Newton's theory of universal gravitation.
The Johannes Kepler University Linz is a public institution of higher education in Austria. It is located in Linz, the capital of Upper Austria. It offers bachelor's, master's, diploma and doctoral degrees in business, engineering, law, science, social sciences and medicine.
Monte Carlo methods are used in corporate finance and mathematical finance to value and analyze (complex) instruments, portfolios and investments by simulating the various sources of uncertainty affecting their value, and then determining the distribution of their value over the range of resultant outcomes. This is usually done by help of stochastic asset models. The advantage of Monte Carlo methods over other techniques increases as the dimensions of the problem increase.
Phelim P. Boyle, is an Irish economist and distinguished professor and actuary, and a pioneer of quantitative finance. He is best known for initiating the use of Monte Carlo methods in option pricing.
The following outline is provided as an overview of and topical guide to finance:
Information-based complexity (IBC) studies optimal algorithms and computational complexity for the continuous problems that arise in physical science, economics, engineering, and mathematical finance. IBC has studied such continuous problems as path integration, partial differential equations, systems of ordinary differential equations, nonlinear equations, integral equations, fixed points, and very-high-dimensional integration. All these problems involve functions of a real or complex variable. Since one can never obtain a closed-form solution to the problems of interest one has to settle for a numerical solution. Since a function of a real or complex variable cannot be entered into a digital computer, the solution of continuous problems involves partial information. To give a simple illustration, in the numerical approximation of an integral, only samples of the integrand at a finite number of points are available. In the numerical solution of partial differential equations the functions specifying the boundary conditions and the coefficients of the differential operator can only be sampled. Furthermore, this partial information can be expensive to obtain. Finally the information is often contaminated by noise.
High-dimensional integrals in hundreds or thousands of variables occur commonly in finance. These integrals have to be computed numerically to within a threshold . If the integral is of dimension then in the worst case, where one has a guarantee of error at most , the computational complexity is typically of order . That is, the problem suffers the curse of dimensionality. In 1977 P. Boyle, University of Waterloo, proposed using Monte Carlo (MC) to evaluate options. Starting in early 1992, J. F. Traub, Columbia University, and a graduate student at the time, S. Paskov, used quasi-Monte Carlo (QMC) to price a Collateralized mortgage obligation with parameters specified by Goldman Sachs. Even though it was believed by the world's leading experts that QMC should not be used for high-dimensional integration, Paskov and Traub found that QMC beat MC by one to three orders of magnitude and also enjoyed other desirable attributes. Their results were first published in 1995. Today QMC is widely used in the financial sector to value financial derivatives; see list of books below.
Gerhard Chroust is an Austrian systems scientist, and Professor Emeritus for Systems Engineering and Automation at the Institute of System Sciences at the Johannes Kepler University Linz, Austria. Chroust is an authority in the fields of formal programming languages and interdisciplinary information management.
Ingo Mörth is an Austrian sociologist.
Günter Pilz is Professor of Mathematics at the Johannes Kepler University (JKU) Linz. Until his retirement in 2013 he was the head of the Institute of Algebra.
The Wittgenstein Award is an Austrian science award supporting the notion that "scientists should be guaranteed the greatest possible freedom and flexibility in the performance of their research." The prize money of up to 1.5 million euro make it the most highly endowed science award of Austria, money that is tied to research activities within the five years following the award. The Wittgenstein-Preis is named after the philosopher Ludwig Wittgenstein and is conferred once per year by the Austrian Science Fund on behalf of the Austrian Ministry for Science.
Quantitative analysis is the use of mathematical and statistical methods in finance and investment management. Those working in the field are quantitative analysts (quants). Quants tend to specialize in specific areas which may include derivative structuring or pricing, risk management, investment management and other related finance occupations. The occupation is similar to those in industrial mathematics in other industries. The process usually consists of searching vast databases for patterns, such as correlations among liquid assets or price-movement patterns.
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets.
Manuel Kauers is a German mathematician and computer scientist. He is working on computer algebra and its applications to discrete mathematics. He is currently professor for algebra at Johannes Kepler University (JKU) in Linz, Austria, and leader of the Institute for Algebra at JKU. Before that, he was affiliated with that university's Research Institute for Symbolic Computation (RISC).
Harald G. Niederreiter is an Austrian mathematician known for his work in discrepancy theory, algebraic geometry, quasi-Monte Carlo methods, and cryptography.
Niyazi Serdar Sarıçiftçi is a Turkish-Austrian physicist. He is professor for physical chemistry at the Johannes Kepler University (JKU) Linz. There, he leads the Institut for Physical Chemistry as well as the Institut for Organic Solar Cells (LIOS).
Sylvia Frühwirth-Schnatter is an Austrian statistician and professor of applied statistics and econometrics at the Vienna University of Economics and Business. She is known for her research in Bayesian analysis. In 2020 she was the President of the International Society for Bayesian Analysis.
Barbara Kaltenbacher is an Austrian mathematician whose research concerns inverse problems, regularization, and PDE-constrained optimization, with applications including the mathematical modeling of piezoelectricity and nonlinear acoustics. She is a Professor of Applied Analysis at the University of Klagenfurt, a member of the Executive Committee of the European Mathematical Society and editor in chief of the Journal of the European Mathematical Society.. Barbara Kaltenbacher has published more than 130 scientific papers and is (co-)author of four monographs.
Hanspeter Mössenböck is an Austrian computer scientist. He is professor of practical computer science and systems software at the Johannes Kepler University Linz and leads the institute of systems software.