To answer this question first i derived the Hessian matrix of $f(x,y)=-\ln(1+\frac{x}{by+a})$ which is as follows:
$$\triangledown^2 f(x,y)=\frac{1}{(by+x+a)^2} \begin{bmatrix} 1 & b \\b & -\frac{b^2x(2by+x+2a)}{(by+a)^2} \end{bmatrix}$$ This matrix is not positive semi definite. Accordingly, i cannot say it is concave function.
On the other hand, $g(x,y)=\frac{x}{by+a}$ is linear-fractional function and $\ln(x)$ is concave function and the composition of a concave function with linear-fractional function is a concave function. Therefore, $f(x,y)=\ln(1+\frac{x}{by+a})$ is concave.
So which one is true, and if it is not concave, is it a non convex problem?