15:15 Christian Bender (Universität des Saarlandes)
Title: A first order backward stochastic partial differential equation for swing option pricing
We study an optimal control problem related to swing option pricing in a general non- Markovian setting in continuous time. As a main result we uniquely characterize the value process in terms of a first-order non-linear backward stochastic partial differential equation (BSPDE).
Under mild assumptions, the value process of the optimal control problem turns out to be continuously differentiable in the space variable (that represents the volume which the holder of the option can still exercise up to maturity). This observation gives rise to an existence and uniqueness result for the corresponding BSPDE in a classical sense. We also explicitly represent the space derivative of the value process in terms of a nonstandard optimal stopping problem over a subset of predictable stopping times. This representation can be applied to derive a dual minimization problem in terms of martingales. The talk is based on joint work with Nikolai Dokuchaev (Curtin University, Perth).
16:45 Frank Riedel (Universität Bielefeld)
Title: Financial Equilibria under Knightian Uncertainty about Volatility
In diffusion models, few suitably chosen financial securities allow to complete the market. As a consequence, the efficient allocations of static Arrow-Debreu equilibria can be attained in Radner equilibria by dynamic trading. We show that this celebrated result generically fails if there is Knightian uncertainty about volatility. A Radner equilibrium with the same efficient allocation as in an Arrow-Debreu equilibrium exists if and only if the discounted net trades of the equilibrium allocation display no ambiguity in the mean. This property is violated generically in endowments, and thus Arrow-Debreu equilibrium allocations are generically unattainable by dynamically trading few long-lived assets.
Im Anschluss findet eine Nachsitzung statt.
More information: www.stochastik.mathematik.uni-mainz.de/rhein-main-kolloquium-stochastik/