Liquidation of an indivisible asset with independent investment

TL;DR

This paper extends explicit solutions for a combined optimal stopping and control problem, analyzing how liquidating an independent indivisible asset impacts investment strategies in a stochastic market with utility preferences.

Contribution

It provides an explicit solution and characterizes the optimal strategy for liquidating an indivisible asset within a stochastic control framework, extending prior models.

Findings

Explicit form of the value function derived

Existence of an optimal stopping-investment strategy proven

Strategy characterized as a limit of explicit maximizing strategies

Abstract

We provide an extension of the explicit solution of a mixed optimal stopping-optimal stochastic control problem introduced by Henderson and Hobson. The problem examines wether the optimal investment problem on a local martingale financial market is affected by the optimal liquidation of an independent indivisible asset. The indivisible asset process is defined by a homogeneous scalar stochastic differential equation, and the investor's preferences are defined by a general expected utility function. The value function is obtained in explicit form, and we prove the existence of an optimal stopping-investment strategy characterized as the limit of an explicit maximizing strategy. Our approach is based on the standard dynamic programming approach.