Abdelrahim Said Mousa

Abstract
We consider a continuous lifetime model for investor whose lifetime is a random variable. We assume the investor has an access to the social welfare system, the financial market and the life insurance market. The investor aims to find the optimal strategies that maximize the expected utility obtained from consumption, investing in the financial market, buying life insurance, registering in the social welfare system, the size of his estate in the event of premature death and the size of his fortune at time of retirement if he lives that long. We use dynamic programming techniques to derive a second-order nonlinear partial differential equation whose solution is the maximum objective function. We use special case of discounted constant relative risk aversion utilities to find an explicit solutions for the optimal strategies. Finally, we have shown a numerical solution for the problem under consideration and study some properties for the optimal strategies.

Abstract

Abstract
We consider the problem faced by a wage-earner with an uncertain lifetime having to reach decisions concerning consumption and life-insurance purchase, while investing his savings in a financial market comprised of one risk-free security and an arbitrary number of risky securities whose prices are determined by diffusive linear stochastic differential equations. We assume that life-insurance is continuously available for the wage-earner to buy from a market composed of a fixed number of life insurance companies offering pairwise distinct life-insurance contracts. We characterize the optimal consumption, investment and life-insurance selection and purchase strategies for the wage-earner with an uncertain lifetime and whose goal is to maximize the expected utility obtained from his family consumption, from the size of the estate in the event of premature death, and from the size of the estate at the time of retirement. We use dynamic programming techniques to obtain an explicit solution in the case of discounted constant relative risk aversion (CRRA) utility functions.

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 tau(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).