We use functional pathwise It\^o calculus to prove a strictly pathwise version of the master formula in Fernholz' stochastic portfolio theory. Moreover, in our setting, the portfolio-generating function may depend on the entire history of the asset trajectories and on an additional continuous trajectory of bounded variation . Our results are illustrated by several examples and shown to work on empirical market data.
We use pathwise It\^o calculus to prove strictly pathwise versions of the master formula in Fernholz' stochastic portfolio theory. Our first version is set within the framework of F\"ollmer's pathwise It\^o calculus and works for portfolios generated from functions that may depend on the current states of the market portfolio and an additional path of finite variation. The second version is formulated within the functional pathwise It\^o calculus of Dupire (2009) and Cont \& Fourni\'e (2010) and allows for portfolio-generating functionals that may depend additionally on the entire path of the market portfolio . Our results are illustrated by several examples and shown to work on empirical market data.
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functional
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a strictly pathwise version
strictly pathwise versions
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Moreover, in our setting, the portfolio-generating function
Our first version is set within the framework of F\"ollmer's pathwise It\^o calculus and works for portfolios generated from functions that
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entire history of the asset trajectories and on an additional continuous trajectory of bounded variation
current states of the market portfolio and an additional path of finite variation. The second version is formulated within the functional pathwise It\^o calculus of Dupire (2009) and Cont \& Fourni\'e (2010) and allows for portfolio-generating functionals that may depend additionally on the entire path of the market portfolio