A Wealth-Dependent Investment Opportunity Set: Its Effect on Optimal Consumption and Portfolio Decisions
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Abstract
We consider a consumption and investment problem where an investor¡¯s investment opportunity gets enlarged when she becomes rich enough, i.e., when her wealth touches a critical level. We derive optimal consumption and investment rules assuming that the investor has a time-separable von Neumann-Morgenstern utility function. An interesting feature of optimal rules is that the investor consumes less and takes more risk in risky assets if the investor expects that she will have a better investment opportunity when her wealth reaches a critical level.Consumption, Investment, Utility function, Brownian motion, Optimal strategy, Investment opportunity, Critical wealth level