STATISTICS FOR REAL TIME BANKING

To my knowledge, mathematics and statistics are insignificantly used as a tool in Banking. 

The truth is that just  the effectiveness of credit decision  and  profit generation depends strictly on mathematics.

Even though , there are laid down procedures like ratio analysis, turnover method assessment, MPBF assessment etc, the statistical concepts are rarely used.

I was wondering, when I joined a bank that correlation and regression are not at all used in Banking. I believe that these will be used at back end for risk assessment but this can be brought as a front line operation before granting a loan.

I believe the credit decision and profitability are directly depended on statistics and math respectively.

Statistics may be applied when we create a system, but are mainly used in the study of the system’s results, with vast data at the past statistics can really be a good tool for banking.

I sincerely declare that I am not blaming/ superseding any of the tools and techniques in place, am just putting up my ideas and believing this should be brought into banking.

Presently I found the following concepts/ theorems will contribute to understanding/ making / determining a finance decision. 

1.Optional stopping theorem

2.Martingale representation theorem

3.Monte Carlo method

4.Value at Risk

5.Brownian Motion

To begin with, let us see how OPTIONAL STOPPING THEOREM will help in credit decisions. Before that let us see some or the applications of stopping theorems

 1) Your own (a stopping time): Let τ denote the time that I'm ruined (i.e. when I have no money left). At any time, I know whether I am ruined or not. For instance, I am not ruined right now. I don't know when ruin occurs, or if it will occur at all, but if it does, I will know.

2) Parking (not a stopping time): Suppose I am driving along a very long road, and that I'm looking for the parking spot which is furthest towards the other end of the road (call this "the last parking spot"). I pass by available spots along the way, but at any time, I never know if I have passed the last free parking spot.

3) My birthday this year (a stopping time): This is a deterministic stopping time. At any time, I know whether or not my birthday has occurred this year. In fact, I know exactly when my birthday occurs, which makes this a non-typical stopping time in the sense that it is deterministic.

With this understanding, Optional stopping theorem can be applied to credit for determining when a working capital limit is to be stopped / reduced - given the internal (excess, ad hoc , SMA, etc) and external factors (Industry scenario, demand and supply etc.

I invite the following reference from math.dartmouth.edu where the stopping theorem is explained as follows

A discrete-time version of the theorem is given below:

Let X = (Xt)t∈ℕ0 be a discrete-time martingale and τ a stopping time with values in ℕ0 ∪ {∞}, both with respect to a filtration (Ft)t∈ℕ0. Assume that one of the following three conditions holds:

(a) The stopping time τ is almost surely bounded, i.e., there exists a constant c ∈ ℕ such that τ ≤ c a.s.

(b) The stopping time τ has finite expectation and the conditional expectations of the absolute value of the martingale increments are almost surely bounded, more precisely,  and there exists a constant c such that  almost surely on the event {τ > t} for all t ∈ ℕ0.

(c) There exists a constant c such that |Xt∧τ| ≤ c a.s. for all t ∈ ℕ0 where ∧ denotes the minimum operator.

Then Xτ is an almost surely well defined random variable and 

Similarly, if the stochastic process X is a submartingale or a supermartingale and one of the above conditions holds, then

for a submartingale, and

for a supermartingale.

The thing is given a set of internal and external conditions discussed earlier, this theorem tell us when a process is to be stopped. 

The application part is under construction in form of a spreadsheet and simulation. After collecting a handful of data and checking the correctness of working, that could be published.

Seeking your assistance for construction of a mathematical model.