An Introduction to Theta-Calculus
19 Pages Posted: 26 Feb 2005
Date Written: February 2005
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.
Keywords: trading strategies, portfolio representation, operator calculus, financial calculus
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