Mark D. Schroder

A term structure model with preferences for the timing of resolution of uncertainty

SummaryIn this paper we present a model of the term structure of interest rates with imperfect information and stochastic differential utility, a form of non-additive recursive utility. A principal feature of recursive utility, that distinguishes it from time-separable expected utility, is its dependence on the timing of resolution of uncertainty. In our model, we parametrize the nonlinearity of recursive utility in a way that corresponds to preferences for the timing of resolution. This way we show explicitly the dependence of prices on the rate of information, as a consequence of the nature of utilities. State prices and the term structure of interest rates are obtained in closed form, and are shown to have a form in which derivative asset pricing is tractable. Comparative statics relating to the dependence of the term structure on the rate of information are also discussed.

Optimality and State Pricing in Constrained Financial Markets with Recursive Utility Under Continuous and Discontinuous Information

We study marginal pricing and optimality conditions for an agent maximizing generalized recursive utility in a financial market with information generated by Brownian motion and marked point processes. The setting allows for convex trading constraints, non-tradable income, and non-linear wealth dynamics. We show that the FBSDE system of the general optimality conditions reduces to a single BSDE under translation or scale invariance assumptions, and we identify tractable applications based on quadratic BSDEs. An appendix relates the main optimality conditions to duality.

Optimal debt contracts and product market competition with exit and entry

We show how competition in oligopolies, with the possibility of failure and exit of a levered incumbent, affects the ex-ante design of optimal debt contracts. When a levered firms profits are unobservable, a debt contract imposes the threat of nonrenewal to induce truthful revelation. Because nonrenewal impacts the future profitability of the surviving competitor, the contract influences the competitors pricing strategy and the equilibrium profits of both firms. The optimal contract is quite different from a standard debt contract, and induces the competitor to be less aggressive, resulting in higher equilibrium prices and profits, and higher returns for investors.

Linked Recursive Preferences and Optimality

We study a class of optimization problems involving linked recursive preferences in a continuous-time Brownian setting. Such links can arise when preferences depend directly on the level or volatility of wealth, in principal-agent (optimal compensation) problems with moral hazard, and when the impact of social influences on preferences is modeled via utility (and utility diffusion) externalities. We characterize the necessary first-order conditions, which are also sufficient under additional conditions ensuring concavity. We also examine applications to optimal consumption and portfolio choice, and applications to Pareto optimal allocations.

The Effects of Competition and Monitoring on R&D Investment: A Dynamic Approach

We examine a dynamic model of R&D investment by competing firms with an uncertain payout and uncertain time to development success. The effect of competition on R&D investment depends critically on whether firms are able to monitor, and react to, each others actions. In the absence of monitoring, competition speeds up investment and erodes option values. When monitoring is allowed, the Pareto-dominant closed-loop equilibrium is identical to the first-best cooperative equilibrium, with investment that is increasingly postponed as more firms enter the market. A novel approach, solving a sequence of pure-jump equilibria, is used to obtain the equilibrium in the Brownian limit.

Information, Imperfect Competition, and Volatility

We show two surprising consequences of introducing endogenous information acquisition into an imperfectly competitive trading model characterized by a small number of traders. First, the marginal value of private information can be negative, resulting in an equilibrium with no private-information acquisition. Second, imperfect competition typically generates information complementarity. We characterize the roles that liquidity traders play in these findings and demonstrate that several polices to improve price efficiency and market liquidity fall short in achieving the intended goals.