1,720,970 research outputs found
Partial regularity of viscosity solutions for a class of Kolmogorov equations arising from mathematical finance
No full textWe study value functions which are viscosity solutions of certain Kolmogorov equations. Using PDE techniques we prove that they are C1+α regular on special finite dimensional subspaces. The problem has origins in hedging derivatives of risky assets in mathematical finance
Optimal Control of Stochastic Delay Differential Equations and Applications to Path-Dependent Financial and Economic Models
Full text linkIn this manuscript we consider a class of optimal control problems of stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we characterize the value function of the problem as the unique viscosity solution of the associated infinite-dimensional Hamilton-Jacobi-Bellman equation. Finally, we prove a C1,\alpha-partial regularity of the value function. We apply these results to path dependent financial and economic problems (Merton-like portfolio problem and optimal advertising)
Second order Hamilton-Jacobi Equations in Hilbert Spaces and Stochastic Boundary Control.
No full textErratum to "A corrected proof of the stochastic verification theorem within the framework of viscosity solutions"
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Verification theorem and construction of epsilon-optimal controls for control of abstract evolution equations
No full textViscosity solutions of dynamic programming equations for optimal control of Navier-Stokes equations.
No full textA Corrected Proof of the Stochastic Verification Theorem within the Framework of Viscosity Solutions
No full textWe present a full and corrected proof of the stochastic verification theorem that was first obtained by Zhou, Yong, and Li [SIAM J. Control Optim., 35 (1997), pp. 243--253]
Hamilton-Jacobi-Bellman Equations for the Optimal Control of the Duncan-Mortensen-Zakai Equation
No full textAbstractWe study a class of Hamilton–Jacobi–Bellman (HJB) equations associated to stochastic optimal control of the Duncan–Mortensen–Zakai equation. The equations are investigated in weighted L2 spaces. We introduce an appropriate notion of weak (viscosity) solution of such equations and prove that the value function is the unique solution of the HJB equation. We apply the results to stochastic optimal control problems with partial observation and correlated noise
On the equivalence of various weak notions of solutions of elliptic PDEs with measurable ingredients.
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