In 1921, John Maynard Keynes and Frank Knight independently insisted on the importance of making a distinction between uncertainty and risk. Keynes referred to matters about which ‘there is no scientific basis on which to form any calculable probability whatever’. Knight claimed that ‘Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated’. Knightian uncertainty exists when people cannot assign probabilities to imaginable outcomes. People might know that a course of action might produce bad outcomes A, B, C, D and E, without knowing much or anything about the probability of each. Contrary to a standard view in economics, Knightian uncertainty is real, and it poses challenging and unresolved issues for decision theory and regulatory practice. It bears on many problems, potentially including those raised by artificial intelligence. It is tempting to seek to eliminate the worst-case scenario, and thus to adopt the maximin rule, which might seem to be the appropriate approach under Knightian uncertainty. But serious problems arise if eliminating the worst-case scenario would (1) impose high risks and costs, (2) eliminate large benefits or potential ‘miracles’ or (3) create uncertain risks.

We study an intertemporal consumption and portfolio choice problem under Knightian uncertainty in which agent’s preferences exhibit local intertemporal substitution. We also allow for market frictions in the sense that the pricing functional is nonlinear. We prove existence and uniqueness of the optimal consumption plan, and we derive a set of sufficient first-order conditions for optimality. With the help of a backward equation, we are able to determine the structure of optimal consumption plans. We obtain explicit solutions in a stationary setting in which the financial market has different risk premia for short and long positions.

The purpose of this paper is to illustrate – in an argumentative style – that once we refrain from the usual neoclassical assumptions and integrate transaction costs, imperfect foresight and bounded rationality into present neoclassical (spot and futures) market theory, we get a more realistic perception of the decentralisation of intertemporal economic decision making. The failure of most futures markets for goods and services is compensated by firms (‘hierarchies’), which are led by entrepreneurs in the sense of Knight (1921) who may be seen as surrogate forward traders of goods and services. We claim that the ‘more realistic assumptions’ of New Institutional Economics, inter alia, provide a better perception of what takes place behind the veil of ‘money and finance’ than neoclassical economics, and why it makes sense to occasionally limit liability and, as a consequence, apply forms of private or public regulation. It might also help to explain some aspects of the financial crisis of 2008.

We study the effects of model uncertainty in a simple New Keynesian model using robust control techniques. Due to the simple model structure, we are able to find closed-form solutions for the robust control problem, analyzing both instrument rules and targeting rules under different timing assumptions. In all cases but one, an increased preference for robustness makes monetary policy respond more aggressively to cost shocks but leaves the response to demand shocks unchanged. As a consequence, inflation is less volatile and output is more volatile than under the nonrobust policy. Under one particular timing assumption, however, increasing the preference for robustness has no effect on the optimal targeting rule (nor on the economy).

A planner and agent in a permanent-income economy cannot observe part of the state, regard their model as an approximation, and value decision rules that are robust across a set of models. They use robust decision theory to choose allocations. Equilibrium prices reflect the preference for robustness and so embody a “market price of Knightian uncertainty.” We compute market prices of risk and compare them with a model that assumes that the state is fully observed. We use detection error probabilities to constrain a single parameter that governs the taste for robustness.