In: Advanced Math
A company offers health insurance to its employees. The insurance pays continuous premiums at the rate of $12,000/year whenever the employee is sick, and nothing otherwise. Suppose that a typical employee gets sick on average every 4 months ,and when sick remains so for an average of 1/2-months. The company constructs an appropriate continuous-time Markov chain to model this situation.
(a) Suppose an employee is healthy today. Find the total expected benefits that she will receive over the next year.