Interbank lending with benchmark rates: Pareto optima for a class of singular control games

We analyze a class of stochastic differential games of singular control, motivated by the study of a dynamic model of interbank lending with benchmark rates. We describe Pareto optima for this game and show how they may be achieved through the intervention of a regulator, whose policy is a solution to a singular stochastic control problem. Pareto optima are characterized in terms of the solutions to a new class of Skorokhod problems with piecewise-continuous free boundary. Pareto optimal policies are shown to correspond to the enforcement of endogenous bounds on interbank lending rates. Analytical comparison between Pareto optima and Nash equilibria provides insight into the impact of regulatory intervention on the stability of interbank rates.Comment: 31 pages; 1 figur

Minimum Guaranteed Payments and Costly Cancellation Rights: A Stopping Game Perspective

We consider the valuation and optimal exercise policy of a δ- penalty minimum guaranteed payment option in the case where the value of the underlying dividend-paying asset follows a linear diffusion. We characterize both the value and optimal exercise policy of the considered game option explicitly and demonstrate that increased volatility increases the value of the option and postpones exercise by expanding the continuation region where exercising is suboptimal. An interesting and natural implication of this finding is that the value of the embedded cancellation rights of the issuer increase as volatility increases.minimum guaranteed payment, δ-penalty options, Dynkin games, linear diffusions

Investment under uncertainty, competition and regulation

We investigate a randomization procedure undertaken in real option games which can serve as a basic model of regulation in a duopoly model of preemptive investment. We recall the rigorous framework of [M. Grasselli, V. Lecl\`ere and M. Ludkovsky, Priority Option: the value of being a leader, International Journal of Theoretical and Applied Finance, 16, 2013], and extend it to a random regulator. This model generalizes and unifies the different competitive frameworks proposed in the literature, and creates a new one similar to a Stackelberg leadership. We fully characterize strategic interactions in the several situations following from the parametrization of the regulator. Finally, we study the effect of the coordination game and uncertainty of outcome when agents are risk-averse, providing new intuitions for the standard case

Competition and Irreversible Investments under Uncertainty

We examine the effect of competition on investment decisions in an industry in which each firm has a completely irreversible investment opportunity and the product market has positive externalities for a small market size and negative externalities for a large market size. In the latter case, which corresponds to the traditional competitive industries, firms invest sequentially as market profitability develops. In the former case, which corresponds to industries in which investment is mutually beneficial, firms invest simultaneously after the market's profitability has developed sufficiently to gain all network benefits and to recover the option value of waiting. These extensions of a real options analysis may help explain rapid and sudden developments such as recent Internet investment, or explain the late take-off phenomenon of prolonged start-up problems, such as the case of fax machine production.Irreversible Investments, Real Options, Network Effects

Irreversible investment in oligopoly

We offer a new perspective on games of irreversible investment under uncertainty in continuous time. The basis is a particular approach to solve the involved stochastic optimal control problems which allows to establish existence and uniqueness of an oligopolistic open loop equilibrium in a very general framework without reliance on any Markovian property. It simultaneously induces quite natural economic interpretation and predictions by its characterization of optimal strategies through first order conditions. The construction of equilibrium policies is then enabled by a stochastic representation theorem. A stepwise specification of the general model leads to further economic conclusions. We obtain explicit solutions for Lévy processes.irreversible investment, stochastic game, oligopoly, real options, equilibrium