Risk-sensitive portfolio optimization problems for hidden Markov factors on infinite time horizon

Article type: Research Article

Authors: Tamura, Takashi^; | Watanabe, Yûsuke^;

Affiliations: Division of Mathematical Science for Social Systems, Graduate School of Engineering Science, Osaka University, Toyonaka 560-8531, Japan. E-mails: {tamura, watanabe}@sigmath.es.osaka-u.ac.jp

Note: [] The present affiliation is: Precursory Research for Embryonic Science and Technology (PRESTO), Japan Science and Technology Agency (JST), 4-1-8 Honcho Kawaguchi, Saitama 332-0012, Japan.

Note: [] Corresponding author. E-mail: [email protected].

Abstract: We consider a market model where risky securities are affected by “hidden” economic factors, which evolve as a finite-state Markov chain. Our problem is optimizing an expected risk-averse power utility of wealth on finite and infinite time horizons. We construct a classical solution of the Hamilton–Jacobi–Bellman equation corresponding to the problem. We also prove some verification theorems.

Keywords: risk-sensitive control, hidden Markov models, Wonham filter, ergodic control

DOI: 10.3233/ASY-2011-1059

Journal: Asymptotic Analysis, vol. 75, no. 3-4, pp. 169-209, 2011