Benoît CHEVALIER-ROIGNANT

There are many business situations in which investments by a supplier and a producer (“coinvestments") are both necessary for either of them to grasp a business opportunity. For instance, better quality tanks are needed to manufacture reliable hydrogen-powered vehicles. One of these two firms, typically the one facing a lower cost, may be more willing to invest, but the cautionary attitude of the other delays the coinvestment. We model supply-chain interactions in a classical tractable way to derive the firms’ net present values (NPVs) upon coinvestment and determine their Nash equilibrium investment (timing) strategies. Firms coinvest when the real options of the weaker firm is ‘deep in the money.’ These business situations are likely to be affected by evolving market circumstances, in particular due to changes in the demand dynamics or endogenous decision (by, say, the supplier) to conduct research and development (R&D). We investigate related model extensions, which confirm the robustness of our key result.

Many cities face challenges in financing their infrastructure. If a decision maker cannot capture all the benefits of its investment, there is a risk of underinvestment. Hong Kong’s transit operator designed a scheme in which it not only receives fare revenues, but also participates in a property management business, exploiting the positive externalities of public transport on nearby property prices. We develop a stochastic Stackelberg game of timing to explore the rationale of this scheme. The underlying problem is nontrivial because the operator faces a two-dimensional optimal stopping problem that cannot be reduced by a change of numéraire. We determine the operator’s optimal investment policy via the intermediation of a “penalized problem” and derive comparative statics. We determine the circumstances under which monetizing positive externalities effectively favors infrastructure investment. Other management problems have similar structures.

We provide an overview of continuous-time processes subject to jumps that do not originate from a compound Poisson process, but from a compound Hawkes process. Such stochastic processes allow for a clustering of self-exciting jumps, a phenomenon for which empirical evidence is strong. Our presentation, which omits certain technical details, focuses on the main ideas to facilitate applications to stochastic control theory. Among other things, we identify the appropriate infinitesimal generators for a set of problems involving various (possibly degenerate) cases of diffusions with self-exciting jumps. Compared to higher-dimensional diffusions, we note a degeneracy of the second-order infinitesimal generator. We derive a Feynman-Kac Theorem for a dynamic system driven by such a jump diffusion and also discuss a problem of continuous control of such a system and provide a verification theorem establishing a link between the value function and a novel type of Hamilton-Jacobi-Bellman (HJB) equation.

Risk-averse entrepreneurs interact with financiers to fund their projects. Projects can be operated under green or dirty technologies. We explore the role of limited commitment in determining the adoption of green technologies when governments enact carbon taxes and/or directed investment subsidies. We show that entrepreneurial (respectively, financier) limited commitment makes it more (less) costly for governments to encourage green technology adoption. Because green technologies are still at an early stage, the cash flows they generate are back-loaded. Entrepreneurial limited commitment forces consumption to increase over time, thereby undermining risk-sharing and making dirty technologies more attractive. By contrast, under financier limited commitment, the possibility that front-loaded dirty technologies become obsolete forces consumption to decrease over time, thereby impairing risk-sharing and making green technologies more attractive. We also show that carbon taxes (directed technology subsidies) are more cost-effective when entrepreneurs (financiers) display limited commitment.

Incumbents can respond to the competitive threat posed by a startup either by external or organic growth. Incumbents may fail do so in due course due to a phenomenon known as “incumbent inertia.” I develop a dynamic model of investment that stresses a new rationale for such inertia. The incumbent may wait even though the option to delay one response is “deep in the money.” This is because the incumbent has to make a choice between several possible responses and is strategically ambivalent about which is best. Such inertia would be bad news for startup valuations if the incumbent delays a lucrative exit for venture capitalists, but good news for consumers if it sustains fiercer competition.

A renewable energy site can expand its power generation capacity by an endogenous amount, but may also want to shut down to save on fixed operating costs and interest payments if the market prospects deteriorate. We model such circumstances and derive managerial implications that help us explain real-world conundrums, illustrating the intricate interactions between the operational decision to build up capacity and the financial decision to exit an industry. Shutting down may be delayed in the hope of expanding capacity upon recovery; expansion may also be delayed in the presence of a valuable exit option. Numerical extensions provide further managerial insights. In particular, the presence of fixed or proportional financing costs may lead the firm to delay its expansion decision, but the scale of investment will only be affected by proportional costs. If herding behavior causes equipment prices to increase (resp., decrease) when electricity prices are high (resp., low), managers should invest earlier (resp., later) and more (resp., less) while equipment prices are low (resp., high). Furthermore, although volume swings (due to capacity decommissionings and expansions) are marked in a homogeneous industry (when the default and expansion thresholds are reached), heterogeneity in the population of wind farms smooths out such effects.

We model the expansion decision of a levered firm. Straight debt distorts both timing and scaling: the firm invests less and later than its all-equity financed counterpart. The inclusion of performance sensitivity in the debt contract mitigates such distortions. Moreover, performance sensitivity is consistent with firm value maximization within a standard trade-off theory of capital structure. As a result, our model rationalizes the widespread use of performance sensitive debt (PSD), especially amongst fast growth firms.

We study capacity investment decisions among oligopoly firms under conditions of cost heterogeneity and output flexibility within capacity constraints. Output flexibility causes the value of the firm to be convex in the state of demand, which implies that the firm invests in larger capacity when the economic environment is more uncertain. Under cost heterogeneity among oligopoly firms, a lower-cost firm invests in larger capacity, while a less efficient rival chooses lower capacity as capacities are strategic substitutes. Consequently, higher uncertainty leads to more dispersion of equilibrium capacities and greater industry concentration. More competition thus induces a welfare loss when uncertainty and cost heterogeneity are high.

We develop a model of oligopoly competition involving innovation effort, market entry and production flexibility under demand uncertainty. Several heterogeneous firms make efforts to develop new prototypes; if they succeed, they hold a shared option to enter a new market under stochastic demand. We derive analytic results for the Markov perfect equilibrium accounting for development effort, market entry and production decisions and complement these by numerical analyses. Firm value—which embeds real options—is not convex increasing in demand but exhibits “competitive waves” due to market entries by rivals. A firm with a development advantage (“innovator”) exerts greater innovation effort if the market is a niche, whereas another benefiting from economies of scale (“incumbent”) invests more if the market is larger. Positive externalities benefit the incumbent in the development stage, whereas the innovator is better off in counteracting negative externalities. Demand volatility raises firm incentives to innovate as it enhances the value of firm market‐entry and production flexibility.

This paper considers a firm’s capacity expansion decisions under uncertainty. The firm has leeway in timing investments and in choosing how much capacity to install at each investment time. We model this problem as the sequential exercising of compound capacity expansion options with embedded optimal capacity choices. We employ the impulse control methodology and obtain a quasi-variational inequality that involves two state variables: an exogenous, stochastic price process and a controlled capacity process (without a diffusion term). We provide a general verification theorem and identify-and prove the optimality of-a two-dimensional (s,S)(s,S)-type policy for a specific (admittedly restrictive) choice of the model parameters and of the running profit. The firm delays investment in capacity to ensure that the perpetuity value of newly installed capacity exceeds the total opportunity cost, including the fixed cost component, by a sufficient margin. Our general model for “the option to expand” transcends a single-option exercise and yields predictions of both the optimal investment timing and the optimal scale of production.