The system [of finance] is too complex to be run on error-strewn hunches and gut feelings, but current mathematical models don’t represent reality adequately. The entire system is poorly understood and dangerously unstable. The world economy desperately needs a radical overhaul and that requires more mathematics, not less.

This article in the Guardian is a little late to the party and has an intentionally misleading headline, but brings up some points that are usually too esoteric to survive in print:

Any mathematical model of reality relies on simplifications and assumptions. The Black-Scholes equation was based on arbitrage pricing theory, in which both drift and volatility are constant. This assumption is common in financial theory, but it is often false for real markets. The equation also assumes that there are no transaction costs, no limits on short-selling and that money can always be lent and borrowed at a known, fixed, risk-free interest rate. Again, reality is often very different.

There are more false assumptions like Gaussianity of log-returns, complete markets, martingale price paths, etc., but these are merely technical complaints, which can be patched (as many are doing). The real issue is, as the author notes, “… instability is common in economic models … mainly because of the poor design of the financial system.” Namely, there is a lack of accounting for behavioral effects that result in feedback, which give rise to rather more fundamental issues that would require the “radical overhaul” alluded to in the opening quotation to resolve. There are some problems that could be tackled in this area.

• Damping: As posed here and here, could damping of price and flow mechanisms in markets create more stability? And at what expense to liquidity or other notions of efficiency? Are there fundamental trade-offs between liquidity and stability — e.g., something like the Gibbs phenomenon in filter design?
• Redundant beliefs: As explained here, risk sharing (e.g. via CDS) stops working when the network of institutions becomes densely connected (and therefore causes short risk feedback cycles.) Is there a way to calculate the correct network risk in a distributed way, by something like iterative message passing, and share that information in a way that does not reveal proprietary information?
• Impact: More generally, price of risk products is set based on some static model of markets, e.g., statistics and predictions assuming things remain the same. However, when risk is mined and sold, it changes the decisions of participants (viz. allowing hedging makes it possible to take larger risks) in a way that could invalidate the data on which pricing was based. Is there a relatively simple, separable model for decision propagation (e.g. a correction term, or an amplification term or filter that modifies a parameter on which the price is based)?

Beyond feedback issues, there are many other questions, such as:

• Heterogeneity: What is the real effect of heterogeneous participants, especially those with different time horizons or risk appetites for asset purchases, on price discovery? What, if any, notion of fairness can we guarantee in these cases? Or, what notion of fairness is actually being computed by standard markets?
• Large systems: How do we pass from small-scale game-theoretic models to large-scale system models? For example, in thermodynamics, we can identify macroscopic variables like temperature with microscopic variables like kinetic energy. Can we identify market variables like volatility with any underlying behavioral variables? What are the “right” (e.g. fundamental, minimal) variables to completely describe a market?
• Instrument design: Are expiring instruments like bonds fundamentally better than infinite-horizons ones like stocks? Can we design market instruments to have certain guarantees on things like volatility? Can we design atomic risk instruments that have payoffs in easy-to-understand terms?

Maybe this list will inspire the field to advance past its current medieval state.

The problem is, China is still only about 40% urbanized (up from about 10% in 1949 and 20% in 1980), and there is a long way to go. Let’s keep in mind that just to get to 50% (a 10% increase) means adding the entire population of Japan to cities, and getting to 70% means adding the entire population of the US. This will take a few decades, and some will come from building new cities or new modes of living. There will be a significant rural population for generations.

On the plains of northern, eastern, and southern China, satellite maps show there is not an inch of land that is not under utilization. Surely population density isn’t as high in rural areas as in cities, relatively speaking, but this is what you get when land is a scarce resource — family plots are only so large, there is no hundred-acre homesteading here, just a unique way toward modern life.

(Rural China. Note: this is not a city, just houses that individual families built for themselves near the land they farm.)

No? Oh it’s money, I see. Except it’s money promised in spam, and spam from the military. How did I get on their list, I wonder. Maybe because of this guy?

Sorry, fellas, but warm, soft direct-deposits from the NSF sounds a lot better, especially because I kind of like my unextreme unadventurous life. And life is the key.

Anyway, forget the publishers. There is one copy in the library, permanently checked out, on hold, or requested. Almost never seen in online stores, it sells for several times the list price when scalper123 occasionally trots it out on YahooMazonBay. Worst of all, nobody has bothered to make and distribute a pdf of it for the good of the masses. Er, wait, I mean, nobody has bothered to make a Fair Use copy for personal use.

And accidentally leave the pdf on an unprotected public server. (Please?)

Well, that was last week, and this is now. I am to this day amazed that Kazoo Books still had one (1) old, used, but perfectly good copy at list price. I wrote “had.” Good service and fast delivery, too. No fraud committed against me despite there being a phone transaction with a credit card. Highly recommend. Wait, this isn’t eBay, why am I writing this?