led by Hansjörg Albrecher and Walter Schachermayer


Re-organization of the Financial Mathematics group:
Group leader: n.n.
Scientific Advisor: Walter Schachermayer

The aim of this research group is the concentration and the further development of different competences to handle problems from mathematical finance and insurance. This includes the development, calibration and analysis of stochastic models for the corresponding real-world processes, questions of optimal choice of control parameters in order to reach a given risk or profitability target and the computational issues relevant for this approach.

Among the topics of current research are portfolio optimization under partial information and under transaction costs, utility maximization in incomplete financial markets (based on duality characterizations of portfolios), valuation and semi-static hedging of financial derivatives in general market models as well as the investigation of risk measures for a surplus process of a portfolio of insurance contracts, both from an analytic and a numerical viewpoint. The sensitivity of risk measures with respect to dependence among the involved risks is studied, which is a highly relevant issue in practical applications.

A further research focus of the group is to investigate bridges between the fields of mathematical finance and actuarial mathematics, both on a methodological and an implementation level. For instance, the transfer of insurance risk into the financial market is a challenging field of research and computational issues of such securitization strategies are addressed. Economic factors such as dividend and tax payments are included in risk models, and stochastic control problems are studied that lead to optimal payment strategies with respect to the specified criteria. Another research direction in this group is to extend the mathematical and probabilistic tools for reinsurance of risks. The complexity of the corresponding problems often does not allow for explicit formulas for the quantities of interest any more. For such situations, efficient rare-event simulation techniques are studied, in particular in the presence of heavy tails for the underlying distributions.

In collaboration with the Inverse Problems group, regularization techniques for parameter calibration of financial market models are investigated, which use the prices of traded instruments in the market. For specific models, alternative parameter estimation procedures based on Markov Chain Monte Carlo techniques are analyzed.

A particular focus of research in the group also lies on the combination of stochastic and number-theoretic methods. Financial mathematics has developed from the classical questions of pricing and hedging of derivative financial instruments to general questions of risk management in financial institutions. Mathematically, this means that models of incomplete markets, as investigated in this group, become more important. One approach is the use of entropy methods, which also appear in inverse problems and non-linear partial differential equations, creating a further link to the other research groups at RICAM. Although the famous Black-Scholes-Formula, honoured by a Nobel prize, is an example for an analytic (= symbolic) solution of a partial differential equation in finance, there usually is no possibility of finding such analytic solutions. One can then either use numerical methods or Quasi-Monte-Carlo Methods, which are a deterministic variant of Monte-Carlo Methods and are based on number-theoretic concepts. These number-theoretic concepts have a great tradition in Austria and are also used in applications outside financial mathematics, e.g. for solving high-dimensional integral and differential equations. Within the group and in combination with other research groups at RICAM, the theory of Monte Carlo- and Quasi-Monte Carlo methods is further developed, which includes complexity reduction issues for high-dimensional integration as well as the generation and analysis of pseudo-random numbers and also addresses problems in coding theory and cryptology.

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The Institute is named after the famous Austrian mathematician Johann Radon (1887-1956)

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Österreichische Akademie der Wissenschaften
Juristische Person öffentlichen Rechts (BGBl 569/1921 idF BGBl I 130/2003)
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