Let B(t) be the cash in the bank, which pays interest at the rate r(t). After a time , the money in the bank will be Re-arranging As the time interval becomes very small, in the limit where it tends to zero we can write Integrating from t to T, for the continuous case which gives Applying the limits and taking the inverse of the log In the continuous case, the growth of an asset at the rate r(t) is given as If the interest rate r(t) is deterministic and a constant (say r), then the eight hand integrand can be completed as (T-t). However, if r(t) is stochastic, then equation (3) is a stochatic equation. Similarly, the stochastic discount factor can be defined as |