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 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...

Subjective evaluations are widely used, but call for different contracts from traditional moral-hazard settings. Previous literature shows that contracts require payments to third parties, which real-world contracts rarely use. I show that the implicit assumption of deterministic contracts makes...

Even though external debt can play a buffer role against adverse shocks to assist consumption smoothing, it may also exert a volatility amplifying effect, depending on the currency of denomination and the cyclicality of the borrower's exchange rate. We empirically investigate the nexus between...

In this chapter, we first discuss the limitations of traditional financial advice, which led to the emergence of robo-advising. We then describe the main features of robo-advising and propose a taxonomy of robo-advisors based on four defining dimensions---personalization, discretion,...

The literature on currency investing that incorporates transaction costs uses costs relevant for small trade sizes. Using the entire order book of the major electronic brokerages for FX, we compute sweep-to-fill costs for trades of different sizes and illustrate the reduction in post-cost...