Optimal timing for the sale of an indivisible asset with jumps: A numerical approach

Abstract

This paper examines the situation in which a utility maximizing agent holds a portfolio composed of a Real Asset and a proportion of a market portfolio. The Real Asset is indivisible, and its sale is irreversible and results in a one-time payment. The question this paper attempts to answer is, “When is the optimal time the agent should sell this Real Asset?”. In other words, at what proportion of the agent’s wealth should the Real Asset be sold. This paper extends the work of Evans et al. (2008) through adding a jump process to the stochastic process of the Real Asset to better capture its idiosyncratic risks. The results can be summarized into three strategies: i) sell immediately, ii) sell at a certain proportion of wealth, and iii) never sell the asset. Furthermore, we have found evidence showing the significance of the addition of the jump process. This addition affects the agent’s optimal path by pushing him to hold on to the Real Asset at smaller fractions of his wealth when compared to the original version of no jumps.