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

by Shinmi Ahn 1 and Hyungbin Park 2,*
1
Graduate School, Kyung Hee University, 6, Kyungheedae-ro, Dongdaemun-gu, Seoul 02453, Korea
2
Department of Mathematical Sciences and RIMS, Seoul National University, 1, Gwanak-ro, Gwanak-gu, Seoul 08826, Korea
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 550; https://doi.org/10.3390/math8040550
Received: 6 February 2020 / Revised: 3 April 2020 / Accepted: 5 April 2020 / Published: 9 April 2020
(This article belongs to the Special Issue Application of Stochastic Analysis in Mathematical Finance)
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. View Full-Text
Keywords: Ross recovery; Sturm–Liouville theory; physical measure; risk-neutral measure; pricing kernel; Markov process Ross recovery; Sturm–Liouville theory; physical measure; risk-neutral measure; pricing kernel; Markov process
MDPI and ACS Style

Ahn, S.; Park, H. Examining the Feasibility of the Sturm–Liouville Theory for Ross Recovery. Mathematics 2020, 8, 550.

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