Finding a stochastic model to describe my life
I would love to write a happy entry on all the fun things I’ve been doing this week, but alas I don’t feel that I can. Instead though, I’m going to combine my creative side with my mathematical side to make some sense of how I’m feeling right now. I hope it all makes sense.
***
Let’s call the start of uni this year time point zero and plot a time series index depicting my overall satisfaction with the state of my life. Imagine if you will, a share price chart, but replace share value with overall satisfaction. Alright, so my overall satisfaction started at the base value of, say, indifferent. Since uni started there was definitely a fluctuating upwards trend in this graph continuing until about week 5, imagine a Brownian motion with positive drift. Around the time of week 5, investors (ie. My mind) started doubting the prosperous progression of the market (ie. My life): it had never happened like this before, surely a constant upwards trend wasn’t sustainable. For a few days though the investors were proved wrong; the trend continued upwards. Tensions were mounting, a flood of papers and articles (ie. My thoughts) were being published about how the trend couldn’t continue upwards until one day in week 6, ‘thwack’ the market crashed. Panic struck investors, the value of the market dropped rapidly and substantially to far below its starting value.
Some investors were optimistic that this was a large fluctuation and that the value would restore in a few days, but the crash continued, amplifying and gaining strength. Bad news events arrived to the market one after the other, until the market finally settled at an overall low level. Aftershocks continued however.
Papers and articles published were numerous, but they all came to the same conclusion. Perhaps a Brownian motion with drift is a poor model for the market, maybe a standard Brownian motion would be better; perhaps value is supposed to fluctuate in a random fashion around the base level of indifferent. Research continues on the issue. It is now widely accepted that the value can be well modelled by a standard Brownian motion process with additional shocks arriving according to a Possion process with parameter lambda and with sizes corresponding to a gamma distribution with parameters alpha and theta.
***
Ok, so you’re probably thinking, huh? What was that all about? Well, it is about time I think that someone expressed themselves in terms of Brownian motions and Poisson processes. Besides, I feel much better now. Until next time, take care and hopefully I will have some good news to report.
I would love to write a happy entry on all the fun things I’ve been doing this week, but alas I don’t feel that I can. Instead though, I’m going to combine my creative side with my mathematical side to make some sense of how I’m feeling right now. I hope it all makes sense.
***
Let’s call the start of uni this year time point zero and plot a time series index depicting my overall satisfaction with the state of my life. Imagine if you will, a share price chart, but replace share value with overall satisfaction. Alright, so my overall satisfaction started at the base value of, say, indifferent. Since uni started there was definitely a fluctuating upwards trend in this graph continuing until about week 5, imagine a Brownian motion with positive drift. Around the time of week 5, investors (ie. My mind) started doubting the prosperous progression of the market (ie. My life): it had never happened like this before, surely a constant upwards trend wasn’t sustainable. For a few days though the investors were proved wrong; the trend continued upwards. Tensions were mounting, a flood of papers and articles (ie. My thoughts) were being published about how the trend couldn’t continue upwards until one day in week 6, ‘thwack’ the market crashed. Panic struck investors, the value of the market dropped rapidly and substantially to far below its starting value.
Some investors were optimistic that this was a large fluctuation and that the value would restore in a few days, but the crash continued, amplifying and gaining strength. Bad news events arrived to the market one after the other, until the market finally settled at an overall low level. Aftershocks continued however.
Papers and articles published were numerous, but they all came to the same conclusion. Perhaps a Brownian motion with drift is a poor model for the market, maybe a standard Brownian motion would be better; perhaps value is supposed to fluctuate in a random fashion around the base level of indifferent. Research continues on the issue. It is now widely accepted that the value can be well modelled by a standard Brownian motion process with additional shocks arriving according to a Possion process with parameter lambda and with sizes corresponding to a gamma distribution with parameters alpha and theta.
***
Ok, so you’re probably thinking, huh? What was that all about? Well, it is about time I think that someone expressed themselves in terms of Brownian motions and Poisson processes. Besides, I feel much better now. Until next time, take care and hopefully I will have some good news to report.
posted by Travvy at 10:25 pm
2 Comments:
Mr Brainy, cant wait to see u back in Melb!!!!!!!
hm...can't say i'm brainy enough to understand it all but i've got the general gist of things *hugs*
...emmy...
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