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Control Optim."],"published-print":{"date-parts":[[2025,4,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>This paper investigates a stochastic linear-quadratic (SLQ) control problem regulated by a time-invariant Markov chain in infinite horizon. Under the [Formula: see text]-stability framework, we study a class of linear backward stochastic differential equations (BSDE) in infinite horizon and discuss the open-loop and closed-loop solvabilities of the SLQ problem. The open-loop solvability is characterized by the solvability of a system of coupled forward-backward stochastic differential equations (FBSDEs) in infinite horizon and the convexity of the cost functional, and the closed-loop solvability is shown to be equivalent to the open-loop solvability, which, in turn, is equivalent to the existence of a static stabilizing solution to the associated constrained coupled algebra Riccati equations (CAREs). Under the uniform convexity assumption, we obtain the unique solvability of associated CAREs and construct the corresponding closed-loop optimal strategy. Finally, we also solve a class of discounted SLQ problems and give two concrete examples to illustrate the results developed in the earlier sections.<\/jats:p>","DOI":"10.1137\/24m1645334","type":"journal-article","created":{"date-parts":[[2025,3,24]],"date-time":"2025-03-24T08:36:10Z","timestamp":1742805370000},"page":"852-891","source":"Crossref","is-referenced-by-count":5,"title":["Stochastic Linear Quadratic Optimal Control Problems with Regime-Switching Jumps in Infinite Horizon"],"prefix":"10.1137","volume":"63","author":[{"given":"Fan","family":"Wu","sequence":"first","affiliation":[{"name":"School of Big Data and Statistics, Anhui University, Hefei, 230601 China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xun","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6670-5351","authenticated-orcid":true,"given":"Xin","family":"Zhang","sequence":"additional","affiliation":[{"name":"Corresponding author. 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