Stochastic compliance–evasion dynamics in tax models: a piecewise deterministic Markov process approach

Battle Count: 53

The paper is entirely focused on tax evasion modelling and socio-economic dynamics. It has no direct connection to quantitative trading, market microstructure, asset pricing, or portfolio management. The PDMP framework is a general stochastic modelling tool, but the specific application (tax compliance) and the model structure (kinetic ODE with sector transitions) are not transferable to trading contexts without substantial modification.

The PDMP simulation requires combining a conserving Euler method (with normalisation at each step) for the n×m-dimensional ODE with a thinning procedure for generating state-dependent jump times. The transition maps (Ψ for audits, Φ for imitation) are straightforward linear reassignments. However, correctly implementing the thinning algorithm, handling the ODE between jumps, managing the state-dependent jump rates, and ensuring conservation properties requires careful numerical work. The illustrative example (n=3, m=2) is tractable, but scaling to larger systems increases complexity. No code is provided.

The paper provides a detailed simulation algorithm (Algorithm 1 in Appendix A), specifies the conserving Euler method with normalisation step (Eq. 17), describes the thinning procedure for PDMP jump times, and gives all model parameters for the illustrative example (n=3 income classes, m=2 evasion sectors, specific tax rates, payment probabilities, initial conditions). However, no code repository is provided, and the paper relies on numerical evidence rather than rigorous analytical proofs for some stationarity claims (Properties 4, Remarks 3, 5, 8).