I am facing an integral equation where one of the terms looks like this:
$$ V(t) = \int_t^{+\infty} K(x-t) \cdot V(x) \, dx $$
where $$K(x) = N(\frac{-b-a\sigma^2}{\sigma \sqrt{x}}) - d^{-2a}N(\frac{-b+a\sigma^2}{\sigma \sqrt{x}}) $$ and $N(\cdot)$ is the cumulative normal distribution. I am inclined to use the Convolution theorem, but the term inside of the $K$ has flipped signs. Also, looking at the formula for $K$ it is not even (nor odd) since its not defined for $x<0$ (Look at the square root term). Any suggestions as to how to make use of the Convolution theorem or any other better way?