{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T14:01:35Z","timestamp":1779890495237,"version":"3.53.1"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2024,2,22]],"date-time":"2024-02-22T00:00:00Z","timestamp":1708560000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,2,22]],"date-time":"2024-02-22T00:00:00Z","timestamp":1708560000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100012306","name":"Universit\u00e0 degli Studi di Trieste","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100012306","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2025,3]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>In this paper, we consider a multi-agent portfolio optimization model with life insurance for two players with random lifetime under a dynamic game approach. Each player is a price-taker and invests in the market to maximize her own utility for consumption and bequest. The market is complete and consists of <jats:italic>n<\/jats:italic> different assets, of which <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$n-1$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>n<\/mml:mi>\n                    <mml:mo>-<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> are risky with prices driven by Geometric Brownian motion, while one is risk-free. We analyze both the non-cooperative and cooperative scenarios, and by considering the family of CRRA utility functions, we determine the closed-form expressions of the optimal consumption, investment, and life insurance for both players. A sensitivity analysis is provided both to illustrate the impact of the biometric and risk aversion parameters on the optimal controls and to compare the non-cooperative strategies with the cooperative ones. As a result, we suggest that cooperation favors the consumption optimality, while non-cooperation promotes the coverage of the risk of death.<\/jats:p>","DOI":"10.1007\/s10479-024-05847-3","type":"journal-article","created":{"date-parts":[[2024,2,22]],"date-time":"2024-02-22T18:02:40Z","timestamp":1708624960000},"page":"1377-1398","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A dynamic game approach for optimal consumption, investment and life insurance problem"],"prefix":"10.1007","volume":"346","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1448-3782","authenticated-orcid":false,"given":"Rosario","family":"Maggistro","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mario","family":"Marino","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Antonio","family":"Martire","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,2,22]]},"reference":[{"key":"5847_CR1","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1016\/j.ejor.2003.10.049","volume":"162","author":"F Ben Abdelaziz","year":"2005","unstructured":"Ben Abdelaziz, F., & Masri, H. 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