Stochastic Volatility Asymptotics for Optimal Subsistence Consumption and Investment with Bankruptcy

23 Pages Posted: 11 Oct 2018 Last revised: 17 Oct 2018

See all articles by Kexin Chen

Kexin Chen

Hong Kong Polytechnic University

Mei Choi Chiu

The Education University of Hong Kong - Department of Mathematics & Information Technology

Yong Hyun Shin

Department of Mathematics, Sookmyung Women's University

Hoi Ying Wong

The Chinese University of Hong Kong (CUHK) - Department of Statistics

Date Written: September 16, 2018

Abstract

Subsistence consumption and investment problems with bankruptcy are classic constrained stochastic optimal control problem in financial economic, where the consumption rate should be greater than a positive number and the investor faces a bankruptcy payment. We derive novel asymptotic solution to this problem under the fast mean-reverting stochastic volatility model. We rigorously prove that the zeroth-order approximation for the optimal pair of consumption and investment strategies leads to the first-order accuracy of the objective function. In addition, this zeroth-order suboptimal consumption-investment pair is asymptotically optimal in a class of admissible trading strategy pairs.

Keywords: optimal investment and consumption, subsistence consumption, stochastic volatility, asymptotic optimality, perturbation

JEL Classification: C61, G11

Suggested Citation

Chen, Kexin and Chiu, Mei Choi and Shin, Yong Hyun and Wong, Hoi Ying, Stochastic Volatility Asymptotics for Optimal Subsistence Consumption and Investment with Bankruptcy (September 16, 2018). Available at SSRN: https://ssrn.com/abstract=3250349 or http://dx.doi.org/10.2139/ssrn.3250349

Kexin Chen (Contact Author)

Hong Kong Polytechnic University ( email )

Hong Kong

Mei Choi Chiu

The Education University of Hong Kong - Department of Mathematics & Information Technology ( email )

Tai Po,, N.T.
Hong Kong

Yong Hyun Shin

Department of Mathematics, Sookmyung Women's University ( email )

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Hoi Ying Wong

The Chinese University of Hong Kong (CUHK) - Department of Statistics ( email )

Shatin, N.T.
Hong Kong

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