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...

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...

This paper considers a general model which allows for both deterministic and stochastic forms of seasonality, including fractional (stationary and nonstationary) orders of integration, and also incorporating endogenously determined structural breaks. Monte Carlo analysis shows that the suggested...

Consider a simple two-state risk with equal probabilities for the two states. In particular, assume that the random wealth variable Xi dominates Yi via ith-order stochastic dominance for i = M,N. We show that the 50-50 lottery [XN + YM, YN + XM] dominates the lottery [XN + XM, YN + YM] via (N +...

This paper provides the proofs to the analysis of a continuous time matching model with saving in Bayer and Wälde (2010a). The paper proves the results on consumption growth, provides an existence proof for optimal consumption and a detailed derivation of the Fokker-Planck equations.

The possibility of low-probability extreme events has reignited the debate over the optimal intensity and timing of climate policy. In this paper we therefore contribute to the literature by assessing the implications of low-probability extreme events on environmental policy in a continuous-time...

In this paper we specify a multi-factor long-memory process that enables us to estimate the fractional differencing parameters at each frequency separately, and adopt this framework to model quarterly prices in three European countries (France, Italy and the UK). The empirical results suggest...

We propose a simple and powerful numerical algorithm to compute the transition process in continuous-time dynamic equilibrium models with rare events. In this paper we transform the dynamic system of stochastic differential equations into a system of functional differential equations of the...

We describe an algorithm that is able to compute the solution of a singular linear difference system under rational expectations. The algorithm uses the Generalized Schur Factorization and is illustrated by a simple example.