A solution to ideal life (L) of a human soul is a function of happiness H (t) that behaves linearly with a positive slope as the independent variable time (t) approaches +ve infinity. For values t < 0 the solutions are undefined unless off course someone finds a solution to the problem of reincarnation R (t).
L = H(t)
L‘ = K ; where K is arbitrary +ve constant usually referred to as karma
But the real life (LR) solution of human beings are almost always nonlinear, which depend on the initial condition (usually known as birth factor), that changes the value of the arbitrary constant K. In most cases H (t) is a trigonometric function with all the ups and downs for t > 0. Sometimes H(t) becomes a quadratic function yielding parabolas with a highest or lowest vertex depending on the initial condition & the value of the arbitrary constant.
Currently research is going on to find exponential solutions for (L) & (LR).
a-jee, i'd probably go with a statistical model with a random process analysis. most of the model's parameters wouldnt be ergodic or even strict sense stationary, no neat Gaussian pdfs for the random variables, but everything would be causal.
of course, one could always take the easy way out by assuming a deterministic model with an outside the box God presetting parameters. in which case, life would be just a train of delta functions through which we wiggle along as a quasi-random path variable.
tsk burgers 