Stochastic volatility asymptotics for optimal subsistence consumption and investment with bankruptcy

Kexin CHEN, Mei Choi CHIU, Yong Hyun SHIN, Hoi Ying WONG

Research output: Contribution to journalArticlespeer-review

Abstract

Subsistence consumption and investment problems with bankruptcy are classic constrained stochastic optimal control problems in financial economics, where the consumption rate should be greater than a positive number and the investor faces a bankruptcy payment. We derive a novel asymptotic solution to this problem under the fast mean-reverting stochastic volatility model. We rigorously prove that the zeroth-order suboptimal pair of consumption and investment strategies leads to the first-order correction of the objective function in the form of v(0) + √ϵv(1). In addition, this zerothorder suboptimal consumption-investment pair is asymptotically optimal in a class of admissible trading strategy pairs. Copyright © 2019 Society for Industrial and Applied Mathematics.
Original languageEnglish
Pages (from-to)977-1005
JournalSIAM Journal on Financial Mathematics
Volume10
Issue number4
Early online dateDec 2019
DOIs
Publication statusPublished - 2019

Citation

Chen, K., Chiu, M. C., Shin, Y. H., & Wong, H. Y. (2019). Stochastic volatility asymptotics for optimal subsistence consumption and investment with bankruptcy. SIAM Journal on Financial Mathematics, 10(4), 977-1005. doi: 10.1137/19M124681X

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