Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Pricing a path-dependent financial derivative, such as an Asian option, requires the computation of E(g(B)), the expectation of a payoff function g, that depends on a Brownian motion B. Employing a standard series expansion of B the latter problem is equivalent to the computation of the expectation of a function of the corresponding i.i.d. sequence of random coefficients. This motivates the construction and the analysis of algorithms for numerical integration with respect to a product probability measure on the sequence space R^N. The class of integrands studied in this paper is the unit ball in a reproducing kernel Hilbert space obtained by superposition of ighted tensor product spaces of functions of finitely many variables. Combining tractability results for high-dimensional integration with the multi-level technique  obtain new algorithms for infinite-dimensional integration. These deterministic multi-level algorithms use variable subspace sampling and they are superior to any deterministic algorithm based on fixed subspace sampling with respect to the respective worst case error.
['Ben Niu', 'Fred J. Hickernell', 'Thomas Müller-Gronbach', 'Klaus Ritter']
I am writing a research paper on a idea Deterministic multi-level algorithms for infinite-dimensional integration on RN
[{"from": "human", "value": "I am writing a research paper on a idea Deterministic multi-level algorithms for infinite-dimensional integration on RN"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Pricing a path-dependent financial derivative, such as an Asian option, requires the computation of E(g(B)), the expectation of a payoff function g, that depends on a Brownian motion B. Employing a standard series expansion of B the latter problem is equivalent to the computation of the expectation of a function of the corresponding i.i.d. sequence of random coefficients. This motivates the construction and the analysis of algorithms for numerical integration with respect to a product probability measure on the sequence space R^N. The class of integrands studied in this paper is the unit ball in a reproducing kernel Hilbert space obtained by superposition of ighted tensor product spaces of functions of finitely many variables. Combining tractability results for high-dimensional integration with the multi-level technique  obtain new algorithms for infinite-dimensional integration. These deterministic multi-level algorithms use variable subspace sampling and they are superior to any deterministic algorithm based on fixed subspace sampling with respect to the respective worst case error."}]