Examining the Feasibility of the Sturm–Liouville Theory for Ross Recovery

Shinmi Ahn and Hyungbin Park
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Shinmi Ahn: Graduate School, Kyung Hee University, 6, Kyungheedae-ro, Dongdaemun-gu, Seoul 02453, Korea
Hyungbin Park: Department of Mathematical Sciences and RIMS, Seoul National University, 1, Gwanak-ro, Gwanak-gu, Seoul 08826, Korea

Mathematics, 2020, vol. 8, issue 4, 1-16

Abstract: Recent studies have suggested that it is feasible to recover a physical measure from a risk-neutral measure. Given a market state variable modeled as a Markov process, the key concept is to extract a unique positive eigenfunction of the generator of the Markov process. In this work, the feasibility of this recovery theory is examined. We prove that, under a restrictive integrability condition, recovery is feasible if and only if both endpoints of the state variable are limit-point. Several examples with explicit positive eigenfunctions are considered. However, in general, a physical measure cannot be recovered from a risk-neutral measure. We provide a financial and mathematical rationale for such recovery failure.

Keywords: Ross recovery; Sturm–Liouville theory; physical measure; risk-neutral measure; pricing kernel; Markov process (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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