Optimal control of inequality under uncertainty

We consider the optimal control of inequality under uncertainty, with a particular focus on income inequality. For an economy experiencing economic growth and random shocks, we show how a simple loss and `bequest' function may be combined to guide the expected level of inequality towards a pre-defined target within a finite planning horizon. Closed form solutions show that, the stronger the shocks to the income distribution, the more aggressive is policy. We discuss the results in the context of recent applied and policy literature on social inequality, globalisation and economic instability.