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A game theoretical approach to homothetic robust forward investment performance processes in stochastic factor models
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Li, Juan, Li, Wenqiang and Liang, Gechun (2021) A game theoretical approach to homothetic robust forward investment performance processes in stochastic factor models. SIAM Journal on Financial Mathematics, 12 (3). pp. 867-897. doi:10.1137/20M1334280 ISSN 1945-497X .
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Official URL: http://dx.doi.org/10.1137/20M1334280
Abstract
This paper studies an optimal forward investment problem in an incomplete market with model uncertainty, in which the underlying stocks depend on the correlated stochastic factors. The uncertainty stems from the probability measure chosen by an investor to evaluate the performance. We obtain directly the representation of the homothetic robust forward performance processes in factor-form by combining the zero-sum stochastic differential game and ergodic BSDE approach. We also establish the connections with the risk-sensitive zero-sum stochastic differential games over an infinite horizon with ergodic payoff criteria, as well as with the classical robust expected utilities for long time horizons. Finally, we give an example to illustrate that our approach can be applied to address a type of robust forward investment performance processes with negative realization processes.
Item Type: | Journal Article | ||||||||||||||||||
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Subjects: | H Social Sciences > HG Finance Q Science > QA Mathematics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||||||||||||
Library of Congress Subject Headings (LCSH): | Stochastic systems, Differential games, Game theory, Ergodic theory , Investment analysis -- Mathematical models | ||||||||||||||||||
Journal or Publication Title: | SIAM Journal on Financial Mathematics | ||||||||||||||||||
Publisher: | Society for Industrial and Applied Mathematics | ||||||||||||||||||
ISSN: | 1945-497X | ||||||||||||||||||
Official Date: | 2021 | ||||||||||||||||||
Dates: |
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Volume: | 12 | ||||||||||||||||||
Number: | 3 | ||||||||||||||||||
Page Range: | pp. 867-897 | ||||||||||||||||||
DOI: | 10.1137/20M1334280 | ||||||||||||||||||
Status: | Peer Reviewed | ||||||||||||||||||
Publication Status: | Published | ||||||||||||||||||
Reuse Statement (publisher, data, author rights): | First Published in SIAM Journal on Financial Mathematics in 12 (3). pp. 867-897 published by the Society for Industrial and Applied Mathematics (SIAM) Copyright © by SIAM. Unauthorized reproduction of this article is prohibited. | ||||||||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||||||||
Date of first compliant deposit: | 6 August 2021 | ||||||||||||||||||
Date of first compliant Open Access: | 9 August 2021 | ||||||||||||||||||
RIOXX Funder/Project Grant: |
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