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Impulse Control in Finance: Numerical Methods and Viscosity Solutions. (arXiv:1712.01647v2 [math.NA] UPDATED)
来源于:arXiv
The goal of this thesis is to provide efficient and provably convergent
numerical methods for solving partial differential equations (PDEs) coming from
impulse control problems motivated by finance. Impulses, which are controlled
jumps in a stochastic process, are used to model realistic features in
financial problems which cannot be captured by ordinary stochastic controls.
The dynamic programming equations associated with impulse control problems
are Hamilton-Jacobi-Bellman quasi-variational inequalities (HJBQVIs) Other than
in certain special cases, the numerical schemes that come from the
discretization of HJBQVIs take the form of complicated nonlinear matrix
equations also known as Bellman problems. We prove that a policy iteration
algorithm can be used to compute their solutions. In order to do so, we employ
the theory of weakly chained diagonally dominant (w.c.d.d.) matrices. As a
byproduct of our analysis, we obtain some new results regarding a particular
family of Markov decis 查看全文>>