Optimal Entry to an Irreversible Investment Plan with Non Convex Costs

TL;DR

This paper investigates the optimal timing for irreversible investment in electricity purchasing when costs are non-convex, leading to complex, irregular entry boundaries due to the non-convex cost structure.

Contribution

It introduces a detailed analysis of the optimal entry policy in non-convex cost scenarios, revealing irregular boundary shapes caused by non-convexity.

Findings

Optimal entry boundary can be irregular and kinked.

Non-convex costs significantly affect investment timing strategies.

The study extends previous models to include non-convex cost considerations.

Abstract

A problem of optimally purchasing electricity at a real-valued spot price (that is, with potentially negative cost) has been recently addressed in De Angelis, Ferrari and Moriarty (2015) [SIAM J. Control Optim. 53(3)]. This problem can be considered one of irreversible investment with a cost functional which is non convex with respect to the control variable. In this paper we study the optimal entry into this investment plan. The optimal entry policy can have an irregular boundary arising from this non convexity, with a kinked shape.