I see lots of papers dealing with application of statistical physics to financial systems. But what are the basic models? There is little point in defining a model, solving it, and finding a answer. Can anybody give me a good starting point?
I guess the two most simple models would be a local/current trend plus one of the two most basic stochastic processes. For the current trend you could assume that the current growth, stagnation or loss is continuing in the near future. The stochastic process is then either Gaussian white noise fitted to the past or the generalisation being alpha-stable noise fitted to the past (Gaussian corresponding to alpha=2).
The basic philosophical question that you have to answer for youself is then the following: Do you assume that sudden jumps in prices are due to single unpredictable events (crises, rumors etc.) that have to be build in by hand later on? (Then you choose Gaussian white noise + manually added jumps.) Or do assume that smaller and larger crises happen from time to time and you want to model how often crises happen and how big they are? (In this case you choose alpha-stable noise with the parameter alpha fitted in a way that the frequency and the typical height of the jumps describe the past well enough.)
These would be the two most simple models that come to my mind.