📘 actuarial science

1. The problem is to understand the concept of the force of mortality, which is a key idea in actuarial science and demography. 2. The force of mortality, denoted by $\mu_x$, is de

1. **Problem statement:** Prove the equation $$\frac{d}{dt} p_x(t) = -p_x(t) \mu_{x+t}$$ where $p_x(t)$ is the probability of survival from age $x$ to $x+t$ and $\mu_{x+t}$ is the

1. **Problem statement:** Harold, aged 60, buys a life annuity paying 1000 annually starting at age 61. The death probability at age 60 is increased by 0.1, i.e., $q_{60}^* = q_{60

1. **Problem Statement:** We want to express an insurance benefit for a 25-year-old that pays 700,000 at the end of the year of death if death occurs before age 50, then the benefi