Originally Posted by

**Frodo** Dear all!

I have some difficulties with estimating parameters. Given a function $\displaystyle P(T)$ with

$\displaystyle P(T) = A\cdot\exp(-B \cdot r),$

where $\displaystyle r$ is a given constant,

$\displaystyle B = B(T,a) = \frac{1-\exp(-a \cdot T)}{a}$

and

$\displaystyle A = A(T,a,b,\sigma) = \exp\left(\frac{(B-T)\cdot(a^2b - \sigma^2/2)}{a^2} - \frac{\sigma^2 B^2}{4a}\right)

$

Let $\displaystyle P^{\mbox{\tiny obs.}}(T)$ be some observed datapoints for (e.g.) $\displaystyle T \in [1,2,3,...,30] $.

I then formulate a target function $\displaystyle \Phi$ by

$\displaystyle \Phi = \min_{a,b,\sigma}\sum\limits_T \left( P(0,T) - P^{\mbox{\tiny obs.}}(0,T)\right)^2

$

Does anybody have a clue how to estimate the parameters $\displaystyle a,b$ and $\displaystyle \sigma$ to solve the problem above?

Thanks for any hint!

Frodo