The virtues and vices of equilibrium and the future of financial economics

The use of equilibrium models in economics springs from the desire for parsimonious models of economic phenomena that take human reasoning into account. This approach has been the cornerstone of modern economic theory. We explain why this is so, extolling the virtues of equilibrium theory; then we present a critique and describe why this approach is inherently limited, and why economics needs to move in new directions if it is to continue to make progress. We stress that this shouldn't be a question of dogma, but should be resolved empirically. There are situations where equilibrium models provide useful predictions and there are situations where they can never provide useful predictions. There are also many situations where the jury is still out, i.e., where so far they fail to provide a good description of the world, but where proper extensions might change this. Our goal is to convince the skeptics that equilibrium models can be useful, but also to make traditional economists more aware of the limitations of equilibrium models. We sketch some alternative approaches and discuss why they should play an important role in future research in economics.Comment: 68 pages, one figur

Comparison of fine structural mice via coarse iteration

Let M be a fine structural mouse. Let D be a fully backgrounded L[E]-construction computed inside an iterable coarse premouse S. We describe a process comparing M with D, through forming iteration trees on M and on S. We then prove that this process succeeds

Leverage Causes Fat Tails and Clustered Volatility

We build a simple model of leveraged asset purchases with margin calls. Investment funds use what is perhaps the most basic financial strategy, called "value investing", i.e. systematically attempting to buy underpriced assets. When funds do not borrow, the price fluctuations of the asset are normally distributed and uncorrelated across time. All this changes when the funds are allowed to leverage, i.e. borrow from a bank, to purchase more assets than their wealth would otherwise permit. During good times competition drives investors to funds that use more leverage, because they have higher profits. As leverage increases price fluctuations become heavy tailed and display clustered volatility, similar to what is observed in real markets. Previous explanations of fat tails and clustered volatility depended on "irrational behavior", such as trend following. Here instead this comes from the fact that leverage limits cause funds to sell into a falling market: A prudent bank makes itself locally safer by putting a limit to leverage, so when a fund exceeds its leverage limit, it must partially repay its loan by selling the asset. Unfortunately this sometimes happens to all the funds simultaneously when the price is already falling. The resulting nonlinear feedback amplifies large downward price movements. At the extreme this causes crashes, but the effect is seen at every time scale, producing a power law of price disturbances. A standard (supposedly more sophisticated) risk control policy in which individual banks base leverage limits on volatility causes leverage to rise during periods of low volatility, and to contract more quickly when volatility gets high, making these extreme fluctuations even worse.Comment: 19 pages, 8 figure

Hyperbolic Discounting Is Rational: Valuing the Far Future with Uncertain Discount Rates

Conventional economics supposes that agents value the present vs. the future using an exponential discounting function. In contrast, experiments with animals and humans suggest that agents are better described as hyperbolic discounters, whose discount function decays much more slowly at large times, as a power law. This is generally regarded as being time inconsistent or irrational. We show that when agents cannot be sure of their own future one-period discount rates, then hyperbolic discounting can become rational and exponential discounting irrational. This has important implications for environmental economics, as it implies a much larger weight for the far future.Hyperbolic discounting, Environment, Time consistent, Exponential discounting, Geometric random walk, Term structure of interest rates

The Virtues and Vices of Equilibrium and the Future of Financial Economics

The use of equilibrium models in economics springs from the desire for parsimonious models of economic phenomena that take human reasoning into account. This approach has been the cornerstone of modern economic theory. We explain why this is so, extolling the virtues of equilibrium theory; then we present a critique and describe why this approach is inherently limited, and why economics needs to move in new directions if it is to continue to make progress. We stress that this shouldn’t be a question of dogma, but should be resolved empirically. There are situations where equilibrium models provide useful predictions and there are situations where they can never provide useful predictions. There are also many situations where the jury is still out, i.e., where so far they fail to provide a good description of the world, but where proper extensions might change this. Our goal is to convince the skeptics that equilibrium models can be useful, but also to make traditional economists more aware of the limitations of equilibrium models. We sketch some alternative approaches and discuss why they should play an important role in future research in economics.Equilibrium, Rational expectations, Efficiency, Arbitrage, Bounded rationality, Power laws, Disequilibrium, Zero intelligence, Market ecology, Agent based modeling

Raman amplification in plasma : thermal effects

The impact of thermal effects on Raman amplification in plasma is investigated theoretically. It is shown that damping and the shift in plasma resonance at finite temperature can alter the evolution of an amplified pulse. It is shown that pulse compression can occur which is not predicted by the cold plasma model. Although thermal effects can lead to a reduction in the efficiency of the interaction, this can be avoided by using a chirped pump. In this case these effects can be beneficial, suppressing the development of a train of pulses behind the amplified seed, as observed in the cold plasma model