We investigate the classical Ramsey problem of economic growth when the planner uses non-constant discounting. It is well-known that this leads to time inconsistency, so that optimal strategies are no longer implementable. We then define equilibrium strategies to be such that unilateral deviations occurring during a small time interval are penalized. Non-equilibrium strategies are not implementable, so only equilibrium strategies should be considered by a rational planner. We show that there exists such strategies which are (a) smooth, and (b) lead to stationary growth, as in the classical Ramsey model. Finally, we prove an existence and multiplicity result: for logarithmic utility and quasi-exponential discount, there is an interval I such that, for every k in I , there is an equilibrium strategy converging to k. We conclude by giving an example where the planner is led to non-constant discount rates by considerations of intergenerational equity.

This paper generalizes, in the setting of Brownian information, the Duffie-Epstein 1992 stochastic differential formulation of intertemporal recursive utility (SDU). We provide a utility functional of state-contingent consumption plans that exhibits a local dependency with respect to the utility intensity process (the integrand of the quadratic variation) and call it the generalized SDU. This mathematical generalization of the SDU permits, in fact, more flexibility in the separation between risk aversion and intertemporal substitution and allows to model asymmetry in risk aversion.We extensively use the backward stochastic differential equation theory to give sufficient conditions for comparative and absolute risk aversion behavior as well as aversion to specific directional risk. Additionally, we discuss whether our functional exhibits monotonicity to its information filtration argument. For purposes of illustration, we provide some applications to the consumption/portfolio strategy selection problem in a complete securities market.

International audienceWe model the debt and asset risk choice of a manager with performance-insensitive pay (cash) and performance-sensitive pay (stock) to theoretically link compensation structure, leverage, and credit spreads. The model predicts that optimal leverage trades off the tax benefit of debt against the utility cost of ex-post asset substitution and that credit spreads are increasing in the ratio of cash-to-stock. Using a large cross-section of U.S.-based corporate credit default swaps (CDS) covering 2001 to 2006, we find a positive association between cash-to-stock and CDS rates, and between cash-to-stock and leverage ratios

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