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http://hdl.handle.net/10397/95632
Title: | Risk-sensitive credit portfolio optimization under partial information and contagion risk | Authors: | Bo, L Liao, H Yu, X |
Issue Date: | Aug-2022 | Source: | Annals of applied probability, Aug. 2022, v. 32, no. 4, p. 2355-2399 | Abstract: | This paper investigates the finite horizon risk-sensitive portfolio optimization in a regime-switching credit market with physical and information-induced default contagion. It is assumed that the underlying regime-switching process has countable states and is unobservable. The stochastic control problem is formulated under partial observations of asset prices and sequential default events. By establishing a martingale representation theorem based on incomplete and phasing out filtration, we connect the control problem to a quadratic BSDE with jumps, in which the driver term is nonstandard and carries the conditional filter as an infinite-dimensional parameter. By proposing some truncation techniques and proving uniform a priori estimates, we obtain the existence of a solution to the BSDE using the convergence of solutions associated to some truncated BSDEs. The verification theorem can be concluded with the aid of our BSDE results, which in turn yields the uniqueness of the solution to the BSDE. | Keywords: | Risk-sensitive control Default contagion Partial observations BSDE with jumps Martingale representation theorem Uniqueness of the solution |
Publisher: | Institute of Mathematical Statistics | Journal: | Annals of applied probability | ISSN: | 1050-5164 | EISSN: | 2168-8737 | DOI: | 10.1214/21-AAP1735 | Rights: | © Institute of Mathematical Statistics, 2022 The following publication Bo, L., Liao, H., & Yu, X. (2022). Risk-sensitive credit portfolio optimization under partial information and contagion risk. The Annals of Applied Probability, 32(4), 2355-2399 is available at https://doi.org/10.1214/21-AAP1735. |
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