 EXPLICIT SOLUTIONS OF CONSUMPTION‐INVESTMENT PROBLEMS IN FINANCIAL MARKETS WITH REGIME SWITCHINGLuz Rocío Sotomayor and Abel Cadenillas Mathematical Finance, 2009, vol. 19, issue 2, 251-279 Abstract: We consider a consumption and investment problem where the market presents different regimes. An investor taking decisions continuously in time selects a consumption–investment policy to maximize his expected total discounted utility of consumption. The market coefficients and the investor's utility of consumption are dependent on the regime of the financial market, which is modeled by an observable finite‐state continuous‐time Markov chain. We obtain explicit optimal consumption and investment policies for specific HARA utility functions. We show that the optimal policy depends on the regime. We also make an economic analysis of the solutions, and show that for every investor the optimal proportion to allocate in the risky asset is greater in a “bull market” than in a “bear market.” This behavior is not affected by the investor's risk preferences. On the other hand, the optimal consumption to wealth ratio depends not only on the regime, but also on the investor's risk tolerance: high risk‐averse investors will consume relatively more in a “bull market” than in a “bear market,” and the opposite is true for low risk‐averse investors. Date: 2009 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:bla:mathfi:v:19:y:2009:i:2:p:251-279 Ordering information: This journal article can be ordered from Access Statistics for this article Mathematical Finance is currently edited by Jerome Detemple More articles in Mathematical Finance from Wiley Blackwell |
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