Constrained Polynomial Likelihood
Caio Almeida and
Paul Schneider
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Caio Almeida: Princeton University
Paul Schneider: University of Lugano - Institute of Finance; Swiss Finance Institute
No 21-45, Swiss Finance Institute Research Paper Series from Swiss Finance Institute
Abstract:
We develop a non-negative polynomial minimum-norm likelihood ratio (PLR) of two distributions of which only moments are known. The PLR converges to the true, unknown, likelihood ratio. We show consistency, obtain the asymptotic distribution for the PLR coefficients estimated with sample moments, and present two applications. The first develops a PLR for the unknown transition density of a jump-diffusion process. The second modifies the Hansen-Jagannathan pricing kernel framework to accommodate polynomial return models consistent with no-arbitrage while simultaneously nesting the linear return model. In the S\&P 500 market, this modification entails sizable positions in option contracts necessary to implement the optimal trading strategy suggested by its dual portfolio formulation.
Keywords: Likelihood ratio; positive polynomial; Reproducing Kernel Hilbert Space (RKHS) (search for similar items in EconPapers)
JEL-codes: C13 C51 C61 (search for similar items in EconPapers)
Pages: 37 pages
Date: 2021-05
New Economics Papers: this item is included in nep-isf
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Persistent link: https://EconPapers.repec.org/RePEc:chf:rpseri:rp2145
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