Finite time-horizon optimal investment and consumption with time-varying subsistence consumption constraints
- Authors
- Jeon, Junkee; Kang, Myungjoo; Shin, Yong Hyun
- Issue Date
- Feb-2021
- Publisher
- SPRINGER JAPAN KK
- Keywords
- Portfolio selection; Time-varying subsistence consumption constraints; Utility maximization; Martingale method; Cauchy problem; Integral transform
- Citation
- JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, v.38, no.1, pp 353 - 377
- Pages
- 25
- Journal Title
- JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS
- Volume
- 38
- Number
- 1
- Start Page
- 353
- End Page
- 377
- URI
- https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/833
- DOI
- 10.1007/s13160-020-00440-0
- ISSN
- 0916-7005
1868-937X
- Abstract
- In this paper we consider a general optimal consumption and portfolio selection problem of a finitely-lived agent whose consumption rate process is subject to time-varying subsistence consumption constraints. That is, her consumption rate should be greater than or equal to some convex, non-decreasing and continuous function of timet. Using martingale duality approach and Feynman-Kac formula, we derive the partial differential equation of the Cauchy problem satisfied by the dual value function. We use the integral transform method for solving this Cauchy problem to obtain the general optimal policies in an explicit form. With constant relative risk aversion and constant absolute risk aversion utility functions we illustrate some numerical results of the optimal policies.
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