A Consumption-Investment Problem with a Diminishing Basket of Goods

Abstract

We consider the problem faced by an economic agent trying to find the optimal strategies for the joint management of her consumption from a basket of K goods that may become unavailable for consumption from some random time i onwards, and her investment portfolio in a financial market model comprised of one risk-free security and an arbitrary number of risky securities driven by a multidimensional Brownian motion. We apply previous abstract results on stochastic optimal control problem with multiple random time horizons to obtain a sequence of dynamic programming principles and the corresponding Hamilton-Jacobi-Bellman equations. We then proceed with a numerical study of the value function and corresponding optimal strategies for the problem under consideration in the case of discounted constant relative risk aversion utility functions (CRRA).

Geometric Approaches and Bifurcations in the Dichotomous Decision Model = الطرق الهندسية والتداخلات في نموذج القرار ذو الحدين

“…The dichotomous decision model has been extended to a general model in [8], and other future extension formulation for the decision model would be to include some kind of stochastic pattern in the model parameters. A recent research articles that handel a stochastic decision problems for individuals introduced by Mousa et al (see [12,13]).…”