We investigate pairwise stochastic comparisons of stationary solutions to the linear recurrence 𝑋𝑡+1=𝐴𝑡𝑋𝑡+𝐵𝑡 , where 𝐴𝑡 and 𝐵𝑡 are non-negative random variables. We establish novel order-preserving properties, which enable us to obtain comparison theorems...

This paper studies a class of stationary mean-field games of singular stochastic control with regime-switching. The representative agent adjusts the dynamics of a Markov-modulated Itô-diffusion via a two-sided singular stochastic control and faces a long-time-average expected profit criterion....

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 present a method for the arbitrage-free interpolation of plain-vanilla option prices and implied volatilities, which is based on a system of integral equations that relates terminal density and option prices. Using a discretization of the terminal density, we write these integral equations as...