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OPTIMAL PORTFOLIO AND CONSUMPTION FOR A MARKOVIAN REGIME-SWITCHING JUMP-DIFFUSION PROCESS

Part of: Mathematical finance Stochastic systems and control Applications

Published online by Cambridge University Press:  21 July 2021

CAIBIN ZHANG Open the ORCID record for CAIBIN ZHANG [Opens in a new window] ,
ZHIBIN LIANG Open the ORCID record for ZHIBIN LIANG [Opens in a new window]  and
KAM CHUEN YUEN Open the ORCID record for KAM CHUEN YUEN [Opens in a new window]
CAIBIN ZHANG*
Affiliation:
School of Finance, Nanjing University of Finance and Economics, Nanjing210023, China
ZHIBIN LIANG
Affiliation:
School of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University, Nanjing210023, China; e-mail: [email protected].
KAM CHUEN YUEN
Affiliation:
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China; e-mail: [email protected].
*
e-mail: [email protected]
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Abstract

We consider the optimal portfolio and consumption problem for a jump-diffusion process with regime switching. Under the criterion of maximizing the expected discounted total utility of consumption, two methods, namely, the dynamic programming principle and the stochastic maximum principle, are used to obtain the optimal result for the general objective function, which is the solution to a system of partial differential equations. Furthermore, we investigate the power utility as a specific example and analyse the existence and uniqueness of the optimal solution. Under the constraints of no-short-selling and nonnegative consumption, closed-form expressions for the optimal strategy and the value function are derived. Besides, some comparisons between the optimal results for the jump-diffusion model and the pure diffusion model are carried out. Finally, we discuss our optimal results in some special cases.

Keywords

portfolio and consumptionjump-diffusion processregime switchingHamilton–Jacobi–Bellman equationstochastic maximum principle

MSC classification

Primary: 62P05: Applications to actuarial sciences and financial mathematics
Secondary: 91G10: Portfolio theory 93E20: Optimal stochastic control
Type
Research Article
Information
The ANZIAM Journal , Volume 63 , Issue 3 , July 2021 , pp. 308 - 332
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Copyright
© Australian Mathematical Society 2021

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