Guess lots of people have run out of patience for the Verizon version of iPhone. And then comes the Droid campaign that vehemently and directly bashes iPhone (Everything iDon’t Droid does), which makes people wonder: will there be an iPhone for verizon customers even in 2010, or worse - ever? This is further complicated by the recent rumor that Verizon is closely cooperating with Apple on releasing the 4G version of iPhone.
Actually if you look at all these together it kind of makes sense, and seems the rumor (of 2010 4G iPhone) could well be true. It is obvious that Verizon wants some bargaining power with Apple in the months to come, and seriously, it is Apple that stands to lose if they don’t get Verizon as a partner.
It is all business. What would benefit Apple most? Not existing sales/relationships, but new sales. It is actually to Apple’s interest if people break contract with AT&T only to buy another iPhone with Verizon (don’t forget that those phones are not interchangeable). This is a very likely scenario given the new regulations on termination fees, and grudges about AT&T. The worst thing for Apple is that people stick with their old iPhone on AT&T. How would that happen? If Verizon and Apple are still “in talks” by next year.
True that Droid’s ad directly points out the weakness of iPhone, but that will only hurt sales of Apple, not of Verizon, because there isn't any worthwhile contestant to iPhone to date. It will hurt the relationship between Verizon and Apple, but does Apple really have a choice? A few billion dollars of new sale - I doubt Apple would forgo that however they hate Verizon.
Wednesday, October 21, 2009
Sunday, October 18, 2009
Short comment on some analyses of this financial crisis
There have been numerous analyses of the current (or “past”) credit crunch, comparing or contrasting it with the 1930 crash. The approach was often putting the DOW JONES time series on top of that of 1930 and discuss the similarities or dissimilarities between the two.
The problem with this approach was - I am shocked that nobody pointed it out - that the fundamental time scales have been changed. The time taken to disseminate market information has been shortened significantly, while other time scales (e.g. intervals between earnings reports, time taken to finalize an M&A deal) have been changed by a more moderate degree, although it is almost certain that all time scales have been shortened. It is hard to fathom which time scales here play a major role in today’s world of finance, but it is understandable that things ought to happen faster now - thus the comparison of stock indexes can not be apple-to-apple.
There is more to the problem. The behavior of dynamic systems is heavily affected by the lineup of its spectrum of modes, and a momentary resonance can lead to a quick breakdown of a recently stable system (to be fair - mathematically it has always been inherently chaotic). The question is, could the evolution of different time scales be the ultimate reason of a breakdown of the financial system?
MORE ON TIME SCALE ANALYSIS
In near-integrable systems, or near-integrable areas, the stability of the system depends heavily on the absence of resonances. In finance, we have this imperfect system in which resonances are multi-dimensional and impossible to capture accurately. However we may indirectly verify this claim by examing the ratio of key time scales - every time they are aligned with small-integer ratios chaos is imminent.
Note that there are two kinds of time scales: dissipative (e.g. time to absorb information) and cyclic; imaginary and real.
MORE ON THE CHAOS MODEL
I am tempted to describe the financial world by a series of elements: resources, assets, and consumption. Denomination is a problem. It is also uncertain whether we should describe the state in a classical or quantum manner. If there are N assets, is the financial space RN or RN×RN? I suspect that the valuation method (i.e. value = dividend/(r-g)) also plays a role in the instability.
The problem with this approach was - I am shocked that nobody pointed it out - that the fundamental time scales have been changed. The time taken to disseminate market information has been shortened significantly, while other time scales (e.g. intervals between earnings reports, time taken to finalize an M&A deal) have been changed by a more moderate degree, although it is almost certain that all time scales have been shortened. It is hard to fathom which time scales here play a major role in today’s world of finance, but it is understandable that things ought to happen faster now - thus the comparison of stock indexes can not be apple-to-apple.
There is more to the problem. The behavior of dynamic systems is heavily affected by the lineup of its spectrum of modes, and a momentary resonance can lead to a quick breakdown of a recently stable system (to be fair - mathematically it has always been inherently chaotic). The question is, could the evolution of different time scales be the ultimate reason of a breakdown of the financial system?
MORE ON TIME SCALE ANALYSIS
In near-integrable systems, or near-integrable areas, the stability of the system depends heavily on the absence of resonances. In finance, we have this imperfect system in which resonances are multi-dimensional and impossible to capture accurately. However we may indirectly verify this claim by examing the ratio of key time scales - every time they are aligned with small-integer ratios chaos is imminent.
Note that there are two kinds of time scales: dissipative (e.g. time to absorb information) and cyclic; imaginary and real.
MORE ON THE CHAOS MODEL
I am tempted to describe the financial world by a series of elements: resources, assets, and consumption. Denomination is a problem. It is also uncertain whether we should describe the state in a classical or quantum manner. If there are N assets, is the financial space RN or RN×RN? I suspect that the valuation method (i.e. value = dividend/(r-g)) also plays a role in the instability.
Friday, January 16, 2009
Men's Room Problem
There are N urinals; men prefer to stand away from others and they come in following a Poisson process and occupy one urinal for a fixed amount of time. How many flushes each of the urinals would get for each day?
COMMENT: this problem gets interesting when N is larger than 3 and the restroom is relatively crowded (say always slightly more than half occupied). Say N=2^n+1, the # of flushes is not a monotonous function from one side to the other; instead as n goes to infinity, it could very well have an asymptotic form like the Weierstrass function (not proved)...
COMMENT: this problem gets interesting when N is larger than 3 and the restroom is relatively crowded (say always slightly more than half occupied). Say N=2^n+1, the # of flushes is not a monotonous function from one side to the other; instead as n goes to infinity, it could very well have an asymptotic form like the Weierstrass function (not proved)...
Wednesday, January 14, 2009
Optimal trading strategy for raising silkworms
Jingles mentioned that when she was a child, she used to trade silkworms for Mulberry leaves because otherwise her worms would starve. Here is the question: what is the optimal trading strategy to have the most living silkworms by day T?
Some basic assumptions:
1, trade is one way only.
2, each silkworm consumes 1 unit of leaf every day.
3, leaves have a half life of k days (2 leaves from k days ago is equivalent to 1 leaf from today).
4, the price formula (# of leaves traded for one worm) is P(t) on day t, for starters, assume P(t) is a constant function.
5, silkworm will starve to death if not fed for one day, however, one can choose which worms to feed (so if leaves are insufficient, at least some of the worms can survive).
Some basic assumptions:
1, trade is one way only.
2, each silkworm consumes 1 unit of leaf every day.
3, leaves have a half life of k days (2 leaves from k days ago is equivalent to 1 leaf from today).
4, the price formula (# of leaves traded for one worm) is P(t) on day t, for starters, assume P(t) is a constant function.
5, silkworm will starve to death if not fed for one day, however, one can choose which worms to feed (so if leaves are insufficient, at least some of the worms can survive).
Monday, January 12, 2009
Stock price a chaotic revelation?
For a process x(t), define survivability ratio P(t) = chance of finding x(t) within a predetermined range of x(0); Brownian motion has P(t) = t^(-1/2). For chaotic systems with Cantori trapping mechanisms, P(t) also follows a power law P(t) = t^(-p), p=1+α, with 0<α<1.
Now, assume s(t) is the drift-adjusted part of the stock price while S(t) is the unadjusted (original) stock price. In other words:
d(lnS(t)) = μ dt + ds(t),
we might be able to check the index α for the process s(t), by sampling a lot of (t=0).
Also Re: self-criticality; people have discussed (with mixed opinions) the relationship between financial markets and earthquakes (Gutenberg-Richter law). It might be worthwhile to check the survivability function of fBm. See also 1/f noises.
Now, assume s(t) is the drift-adjusted part of the stock price while S(t) is the unadjusted (original) stock price. In other words:
d(lnS(t)) = μ dt + ds(t),
we might be able to check the index α for the process s(t), by sampling a lot of (t=0).
Also Re: self-criticality; people have discussed (with mixed opinions) the relationship between financial markets and earthquakes (Gutenberg-Richter law). It might be worthwhile to check the survivability function of fBm. See also 1/f noises.
