Portfolio Selection with Mandatory Bequest

TL;DR

This paper analyzes optimal investment and consumption strategies considering a mandatory bequest, using HJB equations to incorporate transaction costs and boundary constraints, revealing how investors treat bequests as expenses affecting their decisions.

Contribution

It introduces a method to explicitly solve portfolio optimization problems with mandatory bequests and transaction costs using HJB equations.

Findings

Investor treats bequest as an expense in decision-making.

Portfolio proportions are maintained within fixed boundaries.

Explicit solutions are derived for the modified optimization problem.

Abstract

In this paper, optimal consumption and investment decisions are studied for an investor who can invest in a fixed interest rate bank account and a stock whose price is a log normal diffusion. We present the method of the HJB equation in order to explicitly solve problems of this type with modifications such as a fixed percentage transaction cost and a mandatory bequest function. It is shown that the investor treats the mandatory bequest as an expense that she factors into her personal wealth when making consumption and transaction decisions. Furthermore, the investor keeps her portfolio proportions inside a fixed boundary relating to Merton's optimal proportion and the transaction costs.