Martingales versus PDEs in finance: an equivalence result with examples (Q2725292)

There are two main methods to obtain a valuation formula for a given derivative: The martingale approach and the partial differential equation approach. It turns out that it is surprisingly tricky to show that the two approaches are equivalent. The main contribution of the authors is to specify a mixture of analytic and probabilistic assumptions strong enough to allow to prove the equivalence of the two approaches. These assumptions are weak enough to be satisfied in some typical examples from finance. The latter include Heston's stochastic volatility model, the Black-Karasinski term structure model as well as the constant elasticity of variance model introduced by \textit{J. C. Cox} [J. Portfolio Manage., Special Issue Dec. 1996, 15-17 (1996)].