Tax evasion, audits with memory, and portfolio choice

In this study, we consider the memory property of tax audits to investigate the tax evasion problem from the perspective of portfolio choice. We explore the implications of the memory property for tax evasion, consumption, and asset allocation. Assuming that tax audits and jumps in the risky asset both follow self-exciting Hawkes processes, we provide a semi-analytical solution to this problem for an agent with constant relative risk aversion (CRRA) utility. We find that the memory feature does not change the agent's effective holding in the risky asset, and its effects on tax evasion and consumption are determined by the agent's risk aversion. It is suggested that government should treat agents differentially by their risk preferences and set audit-related parameters carefully to avoid unnecessary public expenditure.