This paper provides the mathematical foundation for polynomial diffusions. They play an important role in a growing range of applications in finance, including financial market models for interest rates, credit risk, stochastic volatility, commodities and electricity. Uniqueness of polynomial...

We derive closed form solutions to the discounted optimal stopping problems related to the pricing of the perpetual American standard put and call options in a diffusion model with piecewise-linear coefficients. The method of proof is based on the reduction of the initial optimal stopping...