{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T17:56:35Z","timestamp":1754157395235,"version":"3.41.2"},"reference-count":14,"publisher":"Emerald","issue":"3\/4","license":[{"start":{"date-parts":[[2009,4,10]],"date-time":"2009-04-10T00:00:00Z","timestamp":1239321600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009,4,10]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-heading\">Purpose<\/jats:title><jats:p>The purpose of this paper is to research the optimal portfolio proportion for the optimal investment model and the optimal consumption investment strategies for the optimal consumption investment model under compound\u2010jump processes.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Design\/methodology\/approach<\/jats:title><jats:p>Traditionally, the price of risky security or asset is often modeled as geometric Brownian motion. However, the analysis of stock price evolution reveals sudden and rare breaks logically accounted for by exogenous events on information. It is natural to model such behavior by means of a point process, or, more simply, by a Poisson process, which has jumps of constant size occurring at rare and unpredictable intervals. Assume that the price of risky security stock is modeled by a compound\u2010jump process, the renew process theory is chosen to solve the optimal investment model, the HJB equation is chosen for the optimal consumption investment model.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Findings<\/jats:title><jats:p>Derive the analytical optimal portfolio proportion for the reduction model of optimal investment. The optimal consumption investment strategies are given by some equations for the optimal consumption investment model.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Research limitations\/implications<\/jats:title><jats:p>Accessibility and availability of data are the main limitations which model will be applied.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Practical implications<\/jats:title><jats:p>The results obtained in this paper could be used as a guide to actual portfolio management.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title><jats:p>The new approach for the optimal portfolio model under compound\u2010jump processes. The paper is aimed at actual portfolio managers.<\/jats:p><\/jats:sec>","DOI":"10.1108\/03684920910944245","type":"journal-article","created":{"date-parts":[[2009,5,30]],"date-time":"2009-05-30T07:00:29Z","timestamp":1243666829000},"page":"522-532","source":"Crossref","is-referenced-by-count":2,"title":["Optimal portfolio model under compound jump processes"],"prefix":"10.1108","volume":"38","author":[{"given":"Shuping","family":"Wan","sequence":"first","affiliation":[]}],"member":"140","reference":[{"key":"key2022013120371802400_b4","doi-asserted-by":"crossref","unstructured":"Emmer, S., Klupperlberg, C. and Korn, R. (2001), \u201cOptimal portfolios with bounded capital at risk\u201d, Mathematical Finance, Vol. 11 No. 4, pp. 365\u201084.","DOI":"10.1111\/1467-9965.00121"},{"key":"key2022013120371802400_b7","doi-asserted-by":"crossref","unstructured":"Guo, W. and Xu, C. 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(2000), \u201cGrowth optimal portfolio in a market driven by a jump\u2010diffusion\u2010like process or a levy process\u201d, Annals of Economic and Finance, Vol. 1, pp. 101\u201016."},{"key":"key2022013120371802400_b2","unstructured":"Zhang, P. and Yue, C. (2006), \u201cThe pivoting algorithm on the expected utility portfolio selection model without short sales\u201d, Advances in Systems Science and Applications, Vol. 6 No. 2, pp. 276\u201080."},{"key":"key2022013120371802400_b8","doi-asserted-by":"crossref","unstructured":"Zhang, X. 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