Optimal consumption-investment with critical wealth level

We consider a consumption-investment problem in which the relevant economic conditions change, depending on whether the wealth exceeds a critical level or not. We propose a dynamic programming method to solve the problem by dividing the problem into subproblems split by wealth levels, and imposing a freeze condition at the boundaries. We then join the solutions of the subproblems so that the resulting value function is piecewise C-2. The methodology is illustrated through an application to a problem with nonnegative life insurance constraint. (C) 2016 Elsevier Inc. All rights reserved.11Nsciescopu

A Wealth-Dependent Investment Opportunity Set: Its Effect on Optimal Consumption and Portfolio Decisions

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