Three pillars

Date: 2006-10-26
Ticker: %S
Event:: Read Duffie’s book
Title: Three pillars
Content:

“The three pillars of the theory, arbitrage, optimality and equilibrium, ……”

- Darrell Duffie, “Dynamic Asset Pricing Theory”

This excerpt is a super elucidating explanation on financial theory, both in theory and practice.

Pure arbitrage is only realized when your portfolio eliminate all the uncertain factors. For a more elegant formulation, see the vector space demonstration in Duffie’s book. If not, your portfolio is just hedged.

Optimality is supposed to be the guideline of financial world. Though in behavior financial, they show doubts about whether there is a sure or could-be-derived utility for individual (I totally agree with this point of view in consideration of the extreme unpredictable weird incentive when people buy stocks), there seems to be really an invisible hand when we are making decisions. If we are put in an experimental environment, such effect may be more obvious.

Equilibrium is how the financial machine runs. People want to buy and people want to buy.; equilibrium leads them. Sometimes demand and supply dominates which is often called liquidity. In a more general view, the whole financial world is not some Brownian motion, but a dynamical system at its general equilibrium which is connected by tremendous individual equilibria.

So for arbitrage, we ask is our world really arbitrage free? Despite of correlations among atoms like stocks and bonds, uncontrollable financial innovations such as options, swaps, really make the world complicated.

For optimality, we are wondering the term structure of people’s behaviors. Behind the simplification as Brownian motion, we are looking for more interaction to avoid tragedy like LTCM.

For equilibrium, an interesting question is combined with optimality, is the world more beautiful with financial innovations? With options, it seems option underwriter and buyer are both better off. To be more complicated, the infinite persons’ big game is like a whirlpool. Everyone has the right to make and take any product; every product has its own demand and supply curve. Adding atoms, the game becomes really interesting.