Risk Sensitive Portfolio Optimization with Default Contagion and Regime-Switching
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 recurs...
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creator | Bo, Lijun Liao, Huafu Yu, Xiang |
description | 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 to work in the following procedure: Applying the
theory of monotone dynamical system, 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. |
doi_str_mv | 10.48550/arxiv.1712.05676 |
format | Article |
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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 to work in the following procedure: Applying the
theory of monotone dynamical system, 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.</description><identifier>DOI: 10.48550/arxiv.1712.05676</identifier><language>eng</language><subject>Mathematics - Optimization and Control ; Mathematics - Probability ; Quantitative Finance - Portfolio Management</subject><creationdate>2017-12</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,777,882</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1712.05676$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1712.05676$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Bo, Lijun</creatorcontrib><creatorcontrib>Liao, Huafu</creatorcontrib><creatorcontrib>Yu, Xiang</creatorcontrib><title>Risk Sensitive Portfolio Optimization with Default Contagion and Regime-Switching</title><description>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 to work in the following procedure: Applying the
theory of monotone dynamical system, 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.</description><subject>Mathematics - Optimization and Control</subject><subject>Mathematics - Probability</subject><subject>Quantitative Finance - Portfolio Management</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj8tOwzAURL1hgQofwAr_QIIdx48uUXgUqVKh7T66cez0iiSuElMKX0_ashrNaDSjQ8gdZ2lupGQPMBzxkHLNs5RJpdU1-Vjj-Ek3rh8x4sHR9zBEH1oMdLWP2OEvRAw9_ca4o0_Ow1cbaRH6CM0phr6ma9dg55LNVLE77JsbcuWhHd3tv87I9uV5WyyS5er1rXhcJjAdJ5XKmePaCFuBknPH88kxozhkoq6UF1J4cFzlRmtTe299ZedGM2czldWKixm5v8yemcr9gB0MP-WJrTyziT8FCkqR</recordid><startdate>20171215</startdate><enddate>20171215</enddate><creator>Bo, Lijun</creator><creator>Liao, Huafu</creator><creator>Yu, Xiang</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20171215</creationdate><title>Risk Sensitive Portfolio Optimization with Default Contagion and Regime-Switching</title><author>Bo, Lijun ; Liao, Huafu ; Yu, Xiang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a676-b640e1783cba659e14e170861a23db6f353fae1648778dffcfbc9870ec262d613</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Mathematics - Optimization and Control</topic><topic>Mathematics - Probability</topic><topic>Quantitative Finance - Portfolio Management</topic><toplevel>online_resources</toplevel><creatorcontrib>Bo, Lijun</creatorcontrib><creatorcontrib>Liao, Huafu</creatorcontrib><creatorcontrib>Yu, Xiang</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Bo, Lijun</au><au>Liao, Huafu</au><au>Yu, Xiang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Risk Sensitive Portfolio Optimization with Default Contagion and Regime-Switching</atitle><date>2017-12-15</date><risdate>2017</risdate><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 to work in the following procedure: Applying the
theory of monotone dynamical system, 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.</abstract><doi>10.48550/arxiv.1712.05676</doi><oa>free_for_read</oa></addata></record> |
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subjects | Mathematics - Optimization and Control Mathematics - Probability Quantitative Finance - Portfolio Management |
title | Risk Sensitive Portfolio Optimization with Default Contagion and Regime-Switching |
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