Robust irreversible investment strategy with ambiguity to jump and diffusion risk

• Published date: 01 September 2023
• Author: Shuang Li,Haijun Wang
• Date: 01 September 2023
• DOI: http://doi.org/10.1111/irfi.12413

ORIGINAL ARTICLE

Robust irreversible investment strategy

with ambiguity to jump and diffusion risk

Shuang Li

1

| Haijun Wang

2

1

School of Mathematics, Shanghai University

of Finance and Economics, Shanghai, China

2

School of Mathematics and Shanghai Key

Laboratory of Financial Information

Technology, Shanghai University of Finance

and Economics, Shanghai, China

Correspondence

Haijun Wang, School of Mathematics and

Shanghai Key Laboratory of Financial

Information Technology, Shanghai University

of Finance and Economics, Shanghai, China.

Email: whj@mail.shufe.edu.cn

Funding information

National Natural Science Foundation of China,

Grant/Award Number: 72271250; The

Fundamental Research Funds for the Central

Universities (Shanghai University of Finance

and Economics), Grant/Award Number:

2022110174

Abstract

This paper constructs a robust and irreversible investment

rule applicable to a series of adjacent models. The project

value follows a jump-diffusion process and the investor

exhibits complete ambiguity aversion or partial ambiguity

aversion to the diffusion, jump amplitude, and jump fre-

quency components. The impact of ambiguity aversion with

respect to different components on the optimal investment

strategy is examined. The investment decision is mainly

driven by ambiguity aversion to the jump amplitude rather

than frequency, and an increase in jump intensity leads to

the greater importance of ambiguity aversion to jumps. We

further show that ambiguity aversion regarding jumps plays

a dominant role in determining the investment boundary for

low volatility values, and the influence of ambiguity aver-

sion to the diffusion part gradually outweighs that of ambi-

guity aversion to jumps as volatility grows.

KEYWORDS

ambiguity, irreversible investment, jump-diffusion risk, optimal

investment boundary, the value of investment opportunity

JEL CLASSIFICATION

C61, D81, G31

1|INTRODUCTION

The great majority of investments have the following critical characteristics: (1) the future return on investment is

uncertain; (2) the investment is irreversible because the sunk cost cannot be recovered; (3) the investment

Received: 11 March 2022 Revised: 14 December 2022 Accepted: 29 January 2023

DOI: 10.1111/irfi.12413

© 2023 International Review of Finance Ltd.

International Review of Finance. 2023;23:645–665. wileyonlinelibrary.com/journal/irfi 645

opportunity will not vanish at once and the investment may be postponed, making when to invest a critical decision.

The decision maker has the option of waiting for new information on prices, costs, and other beneficial market fac-

tors. The traditional net present value (NPV) principle uses the net present value as the decision-making standard for

investing or refusing to engage in a project. That is to say, if the present value of future cash flow of the project is

greater than the cost, the project should be funded. The third feature that investments may be delayed invalidates

the NPV principle which ignores the opportunity cost and gives up the option of waiting for new information and

investing in the future. Based on the classic continuous-time model proposed by McDonald and Siegel (1986), invest-

ment under uncertainty has become a significant part of modern economics and finance. Caballero (1991) developed

a model with a cost-of-adjustment mechanism and focused his attention on adjustment costs and irreversibility. Dixit

and Pindyck (1994) figured out the value of investment opportunity for a project subject to Geometric Brownian

Motion using the technique of dynamic programming and contingent claims (option pricing), so as to determine the

optimal investment rule.

Rather than the uncertainty of the probability measure itself, the uncertainty incorporated by most modelsis the

uncertainty of future project returns and market conditions, which is often measured by parameters in a fixed proba-

bility space. In practice, however, the specific distribution is frequently based on assumptions made by experts, and

parameters are estimated using historical data. Economic agents perceive economic models as approximations of the

real model, as Hansen and Sargent (2001), Anderson et al. (2003) and Cogley et al. (2008) pointed out. They think

that economic data is derived from an unidentified member of a group of unspecified models close to the approxi-

mate model. The decision maker may not have a clear understanding of probability and may not be sure what the

real probability is. Knight (1921) first distinguished “measurable uncertainty”or “risk”from “unmeasurable uncer-

tainty”. The former can be simplified into a single probability measure with known parameters, whereas the latter

refers to a situation where the information is too ambiguous to be adequately summarized by a single probability dis-

tribution, which is now referred to as “Knightian uncertainty”or “ambiguity”. Nishimura and Ozaki (2007) analyzed

the irreversible investment decision under Knightian uncertainty for the first time. They studied the value of invest-

ment opportunity under a specific type of Knightian uncertainty –κ-ignorance. They also respectively expounded

the influence of Knightian uncertainty and the traditional uncertainty “risk”on the optimal investment rule. The irre-

versible investment strategy under ambiguity has attracted much interest since then (see Alvarez & Koskela, 2008;

Ma & Niu, 2019; Riedel & Su, 2011). Ma and Niu (2019) investigated the effect of Knightian uncertainty on a firm's

endogenously determined intensity and timing decisions. Market incompleteness was interpreted as a source of

ambiguity about the proper no-arbitrage discount factor and the problem of irreversible investment with idiosyn-

cratic risk was studied by Thijssen (2011). The range of the density generator was limited to κ,κ½to control the

deviation between the new and original measures in the above papers. However, there are certain limitations in

restricting the range of alternative measures depending on the value of κ. Miao and Wang (2011) analyzed option

exercise decisions, in which the agent is ambiguous about a state process that influences the continuation and termi-

nation payoffs. Flor and Hesel (2015) analyzed a firm's investment problem when the dynamics of project value and

investment cost are ambiguous and took ambiguity aversion into account. However, the models they considered

were continuous and jumps were ignored.

We fill this gap and first consider the irreversible investment problem of an investor who is uncertain about the

drift of the project value and about the intensity and amplitude of jumps simultaneously. We show that there are

pronounced differences between ambiguity aversion with respect to different components. On the one hand, ambi-

guity aversion to jump amplitude plays a dominant role in determining the optimal investment rules while ambiguity

aversion to jump frequency shows little impact. In more detail, we propose three cases of partial ambiguity, in which

the decision maker is uncertain about the jump amplitude, jump frequency, or diffusion component and has enough

confidence in the rest, allowing us to compare the relative importance of ambiguity aversion to different compo-

nents. We reveal that greater ambiguity aversion reduces the value of investment opportunity thereby lowering the

optimal investment boundary. On the other hand, the importance of ambiguity aversion to the jump component and

the diffusion component is closely related to jump intensity and volatility. For low volatility values, ambiguity

646 LI and WANG