Tax compliance with uncertain income: a stochastic control model

This paper examines the compliance behaviour of a taxpayer endowed with a stochastic income, taking into account dynamical factors as public and private investments, within a stochastic control framework. Assuming logarithmic utilities and thanks to a suitable rewrite of the problem, we provide an existence and uniqueness result for the solution of the Hamilton–Jacobi–Bellman equation associated to the control problem, and we rely on a symbolic and numerical algorithm to study its solution. Moreover, we implement a Monte Carlo simulation in order to determine an estimate of the mean and the variance of the total declared income together with a confidence interval. To illustrate how the method works, we present a computational example where we assign values to the parameters. In this case we perform a sensitivity analysis, showing how the total declared income is affected by public and private investments, probability of being discovered, fine, tax rate and income uncertainty.