Investment and Exit under Uncertainty with Utility from Anticipation

• Published date: 01 September 2018
• Author: Jinqiang Yang,Jianjun Du,Zhentao Zou
• DOI: http://doi.org/10.1111/irfi.12154
• Date: 01 September 2018

Investment and Exit under

Uncertainty with Utility from

Anticipation*

JIANJUN DU

†

,JINQIANG YANG

‡

AND ZHENTAO ZOU

§

†

School of Social Management, Shanghai University of Political Science and Law,

Shanghai, China

‡

Shanghai Key Laboratory of Financial Information Technology, School of Finance,

Shanghai University of Finance and Economics, Shanghai, China and

§

School of Finance, Shanghai University of Finance and Economics, Shanghai, China

ABSTRACT

This paper explores investmentand exit decisions under uncertainty when the

entrepreneur has anticipatory utility, which leads to the time-inconsistency

problem. Our model predicts that anticipatory utility has ambiguous effectson

the investment strategy, which depends on the form of the project’spayoff.

Under a lump-sum payoff, an entrepreneur with anticipatory utility will

under-invest. However, she prefers over-investing if the project delivers a flow

payoff. Moreover, the model predicts that an entrepreneur with anticipatory

utility is more reluctantto abandon an existing project. Finally, our modelpro-

vides theoretical support and alternative explanation for the empirical evi-

dence that people procrastinate to terminate projects from the perspective of

time-inconsistentpreferences.

JEL Codes: D81; G02; G11

I. INTRODUCTION

In modern economics and finance, the standard real options framework

(Brennan and Schwartz 1985; McDonald and Siegel 1986) has become a basic

tool with a number of applications.

1

Most literature in this field assume that

the agents have standard preferences, which means a person’s instantaneous

utility depends solely on her current consumption level. However, this assump-

tion has been challenged by habit-formation models (Abel 1990; Campbell and

* Jianjun Du is supported by the China Postdoctoral Science Foundation (2015M571463). Jinqiang

Yang acknowledges the support from the National Natural Science Foundation of China (71202007,

71522008, and 71772112), Innovative Research Team of Shanghai University of Finance and Eco-

nomics (2016110241), and Fok Ying-Tong Education Foundation of China (151086). Zhentao Zou is

supported in part by the National Natural Science Foundation of China (71401095/G0115).

1 Majd and Pindyck (1987) extend the basic model with a time-to-build feature. Dixit (1989)

considers entry and exit decisions under uncertainty. Grenadier (1996, 2002) and Grenadier

and Malenko (2011) consider the real options problem in a game-theoretic environment.

© 2017 International Review of Finance Ltd. 2017

International Review of Finance, 18:3, 2018: pp. 359–377

DOI: 10.1111/irfi.12154

Cochrane 1999), in which a person’s current instantaneous utility is affected by

her past consumption level. Habit-formation models help to resolve many

asset-pricing anomalies and have become an essential part of modern asset

pricing.

However, the impact of future consumption on current instantaneous

utility has not received sufficient attention. This idea is formally developed

by Loewenstein (1987). In the first part of his paper, he conducts a surve y

and finds that the subjects are willing to pay less to experience an immedi-

ate kiss than a kiss delayed by 3 days. Since this observation contradicts

standard preferences, he argues that this anomaly can be resolved by antici-

patory utility, namely, that expectations about the future can affect current

instantaneous utility. In the second part of Loewenstein (1987), he forma-

lizes this idea by considering a consumption timing problem in a determin-

istic setting and finds that delaying desired consumption may increase the

agent’s well-being.

In contrast to the deterministic setting in Loewenstein (1987), our paper

embeds anticipatory utility into the standard real options model. We intend to

investigate how an entrepreneur’s investment and exit decisions can be dis-

torted by the existence of anticipatory utility. The entrepreneur’s anticipatory

utility depends on her investment decision, which is chosen to maximize total

lifetime utility; thus we solve the model by backward induction. Specifically, we

first suppose an investment trigger and derive the anticipatory utility, and then

we obtain the entrepreneur’s total lifetime utility. Finally, we solve for the equi-

librium investment policy.

In this paper, we consider both the optimal investment and exit problems

under uncertainty. For the investment problem, we discuss the lump-sum and

flow payoff cases. Under the lump-sum payoff case, an entrepreneur with antic-

ipatory utility invests later than her counterpart in the benchmark case. Since

anticipatory utility exists only before the execution of the option, the entrepre-

neur is reluctant to invest in the project. Moreover, we find that the value of

the option to wait can be negative. In the standard real options model, the

value of the option to wait should be always nonnegative, since the entrepre-

neur is free to choose the investment timing. However, in the presence of antic-

ipatory utility, the entrepreneur’s actions suffer from the time-inconsistency

problem (Strotz 1956; Thaler 1981). Thus, the equilibrium investment policy

may not be optimal under certain circumstances, which allows for the possibil-

ity that the value of the option to wait is negative.

Then, we consider the flow payoff case and find that an entrepreneur with

anticipatory utility invests earlier than her counterpart in the benchmark case.

The time-inconsistency problem also exists in the flow payoff case. Since the

entrepreneur receives more utility from anticipation after exercising the option,

she prefers over-investing if the project delivers a flow payoff.

In addition to the investment problem, we investigate the exit problem

under uncertainty. With the consideration of operating costs, the entrepreneur

will abandon the project when the flow payoff is sufficiently low. We find that

© 2017 International Review of Finance Ltd. 2017360

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