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An Introduction to Theta-calculus


Stefan Dirnstorfer


Thetaris

February 2005



Abstract:     
Theta-calculus is a mathematical calculus for the description of sequential processes, financial contracts and multiperiod strategies in game theory. This calculus allows the explicit notation of all trading strategies and financial products, that can currently not be written in an explicit mathematical form. All kinds of contracts, strategies and multiperiod games can then be captured in terms of their quantitative implications by a vocabulary of three basic effects: Waiting, transacting and deciding. Each elementary activity is represented by an operator, that can be interpreted in an operator sequence as a chronologically ordered list of events. The operator term also represents an explicit formula for the evaluation of the respective strategy's final result. Theta-calculus is especially useful for the notation of financial products, many of which can currently not be represented explicitly. Thus, it places itself as an alternative to the methods of stochastic analysis as well as some technical standards, that aim for a representation of sequential processes and financial products.

Number of Pages in PDF File: 19

Keywords: trading strategies, portfolio representation, operator calculus, financial calculus

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Date posted: February 26, 2005  

Suggested Citation

Dirnstorfer, Stefan, An Introduction to Theta-calculus (February 2005). Available at SSRN: http://ssrn.com/abstract=673504 or http://dx.doi.org/10.2139/ssrn.673504

Contact Information

Stefan Dirnstorfer (Contact Author)
Thetaris ( email )
Leopoldstr. 244
Munich, 80807
Germany
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