We introduce a computational framework for dynamic portfolio valuation and risk management building on machine learning with kernels. We learn the replicating martingale of a portfolio from a finite sample of its terminal cumulative cash flow. The learned replicating martingale is given in closed form thanks to a suitable choice of the kernel. We develop an asymptotic theory and prove convergence and a central limit theorem. We also derive finite sample error bounds and concentration inequalities. Numerical examples show good results for a relatively small training sample size.
We introduce a simulation method for dynamic portfolio valuation and risk management building on machine learning with kernels. We learn the dynamic value process of a portfolio from a finite sample of its cumulative cash flow. The learned value process is given in closed form thanks to a suitable choice of the kernel. We show asymptotic consistency and derive finite sample error bounds under conditions that are suitable for finance applications. Numerical experiments show good results in large dimensions for a moderate training sample size.
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computational framework
simulation method
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replicating martingale
dynamic value process
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terminal
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replicating martingale
value process
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develop an asymptotic theory and prove convergence and a central limit theorem. We also
show asymptotic consistency and
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and concentration inequalities. Numerical examples
under conditions that are suitable for finance applications. Numerical experiments
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for a relatively small
in large dimensions for a moderate