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arXiv · 1411.2950

Algebraic Form of Malliavin Calculus: Creation-Annihilation Operators, Conserved Currents and All That

Peter B. Lerner
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Abstract

The extremely useful method of Malliavin calculus has not yet gained adequate popularity because of the complicated analytic apparatus of this method. The author attempts here to propose a simplified algebraic formalism similar to Malliavin calculus, but based on the notion of creation-annihilation operators instead of Malliavin derivative to replace analytic theorems with algebraic computations. Three test problems: the valuation of portfolio with stochastic payoff function, the expression of the terminal payoff through stochastic integral and the approximate equation for the high-frequency market measure are discussed in Appendices.

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BibTeXRIS

Peter B. Lerner. 2014-11-11. Algebraic Form of Malliavin Calculus: Creation-Annihilation Operators, Conserved Currents and All That. https://arxiv.org/abs/1411.2950

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