Risk sensitive portfolio optimization with default contagion and regime-switching

Lijun Bo, Huafu Liao, Xiang Yu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)

Abstract

We study an open problem of risk-sensitive portfolio allocation in a regime-switching credit market with default contagion. The state space of the Markovian regime-switching process is assumed to be a countably infinite set. To characterize the value function, we investigate the corresponding recursive infinite-dimensional nonlinear dynamical programming equations (DPEs) based on default states. We propose working in the following procedure: Applying the theory of monotone dynamical systems, we first establish the existence and uniqueness of classical solutions to the recursive DPEs by a truncation argument in the finite state space. The associated optimal feedback strategy is characterized by developing a rigorous verification theorem. Building upon results in the first stage, we construct a sequence of approximating risk-sensitive control problems with finite states and prove that the resulting smooth value functions will converge to the classical solution of the original system of DPEs. The construction and approximation of the optimal feedback strategy for the original problem are also thoroughly discussed.

Original languageEnglish
Pages (from-to)366-401
Number of pages36
JournalSIAM Journal on Control and Optimization
Volume57
Issue number1
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • Countably infinite states
  • Default contagion
  • Recursive dynamical programming equations
  • Regime switching
  • Risk-sensitive control
  • Verification theorems

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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