Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/89350
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Title: Risk sensitive portfolio optimization with default contagion and regime-switching
Authors: Bo, L
Liao, H
Yu, X 
Issue Date: 2019
Source: SIAM journal on control and optimization, 2019, v. 57, no. 1, p. 366-401
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.
Keywords: Countably infinite states
Default contagion
Recursive dynamical programming equations
Regime switching
Risk-sensitive control
Verification theorems
Publisher: Society for Industrial and Applied Mathematics
Journal: SIAM journal on control and optimization 
ISSN: 0363-0129
EISSN: 1095-7138
DOI: 10.1137/18M1166274
Rights: © 2019, Society for Industrial and Applied Mathematics.
Posted with permission of the publisher.
The following publication Bo, L., Liao, H., & Yu, X. (2019). Risk sensitive portfolio optimization with default contagion and regime-switching. SIAM Journal on Control and Optimization, 57(1), 366-401 is available at https://dx.doi.org/10.1137/18M1166274
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