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We establish a stochastic control representation for $L^p$-norms on Wiener space. For every $p\ge1$ and every non-negative universally measurable functional $\varphi$, we show that $$\|\varphi(W)\|_p = \sup_a \mathbb{E}\Big[ e^{-\frac12\int_0^T\|a_t\|^2\,dt} \varphi\Big( W+\sqrt{p-1}\int_0^\cdot a_t\,dt \Big) \Big],$$...
The objective of this paper is to investigate the connection between penalty functions from stochastic optimal control, convex semigroups from analysis, and convex expectations from probability theory. Our main result provides a one-to-one relation between these objects. As an application, we use the representation via...
We develop a PDE-based methodology for pricing and hedging European contingent claims in general one-dimensional diffusion markets characterized solely by their scale function and speed measure, possibly without a classical SDE representation, and with constant interest rate. We derive a hedging equation whose solution...
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