arXiv subjects

Iryna Voloshchenko

Publications and source records attributed to Iryna Voloshchenko.

3 recordsLinked to original sources

arXiv2018

Model-free portfolio theory and its functional master formula

We use pathwise Itô calculus to prove two strictly pathwise versions of the master formula in Fernholz' stochastic portfolio theory. Our first version is set within the framework of Föllmer's pathwise Itô 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 Itô calculus of Dupire (2009) and Cont \& Fournié (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.

q-fin.PM↗

arXiv2018

The associativity rule in pathwise functional Itô calculus

In this paper we establish the associativity property of the pathwise Itô integral in a functional setting for continuous integrators. Here, associativity refers to the computation of the Itô differential of an Itô integral, by means of the intuitive cancellation of the Itô differential and integral signs.

math.PR↗

arXiv2016

Pathwise no-arbitrage in a class of Delta hedging strategies

We consider a strictly pathwise setting for Delta hedging exotic options, based on Föllmer's pathwise Itō calculus. Price trajectories are $d$-dimensional continuous functions whose pathwise quadratic variations and covariations are determined by a given local volatility matrix. The existence of Delta hedging strategies in this pathwise setting is established via existence results for recursive schemes of parabolic Cauchy problems and via the existence of functional Cauchy problems on path space. Our main results establish the nonexistence of pathwise arbitrage opportunities in classes of strategies containing these Delta hedging strategies and under relatively mild conditions on the local volatility matrix.

q-fin.MF↗