LaTeX Rendering Demo

A quick test of mathematical typesetting in the digital garden.

Inline math

The loss ratio is $LR=\frac{\text{Incurred Losses}}{\text{Earned Premium}}$.

Block equations

The Poisson distribution, commonly used in frequency modeling:

$$P(N=k)=\frac{{\lambda }^k{e}^{-\lambda }}{k!}$$

GLM link function

In a GLM for insurance pricing, we often use the log link:

$$\ln ({\mu }_i)={\beta }_0+{\beta }_1{x}_{i1}+{\beta }_2{x}_{i2}+\cdots +{\beta }_p{x}_{ip}$$

where ${\mu }_i=E[Y_i]$ is the expected claim frequency or severity for risk $i$.

Chain Ladder

The basic chain ladder development factor:

$$f_k=\frac{{\sum }_{i=1}^{n-k}{C}_{i,k+1}}{{\sum }_{i=1}^{n-k}{C}_{i,k}}$$

---

Back to Welcome