This paper introduces the probabilistic formulation of continuous-time economic models: forward stochastic differential equations (SDE) govern the dynamics of backward-looking variables, and backward SDEs capture that of forward-looking variables. Deep learning streamlines the search for the...

We survey directors and investors on the objectives, constraints, and determinants of CEO pay. 67% of directors would sacrifice shareholder value to avoid controversy on CEO pay, implying they face significant constraints other than participation and incentive compatibility. These constraints...

We study the interplay between tenure decisions, stock market investment and the public social security system. Housing equity not only serves a dual purpose as a consumption good and as an asset, but also provides insurance to buffer various risks in retirement. Our life cycle model captures...

We develop a financial-economic model for carbon pricing with an explicit representation of decision making under risk and uncertainty that is consistent with the Intergovernmental Panel on Climate Change’s sixth assessment report. We find that this approach provides economic support for the...

This article studies the equivalence between labor and consumption taxes in a stochastic context, where the government can undertake an active portfolio management strategy by investing in both risk-free and risky assets. Using a two-period model we show that such taxes let consumers make the...

Using the Hamilton-Jacobi-Bellman equation, we derive both a Keynes-Ramsey rule and a closed form solution for an optimal consumption-investment problem with labor income. The utility function is unbounded and uncertainty stems from a Poisson process. Our results can be derived because of the...