Existence and uniqueness of viscosity solutions for QVI associated with impulse control of jump-diffusions

By R. Seydel. 2009

59 citations recorded by the source corpus.

General theorems for existence and uniqueness of viscosity solutions for Hamilton-Jacobi-Bellman quasi-variational inequalities (HJBQVI) with integral term are established. Such nonlinear partial integro-differential equations (PIDE) arise in the study of combined impulse and stochastic control for jump-diffusion processes. The HJBQVI consists of an HJB part (for stochastic control) combined with a nonlocal impulse intervention term. Existence results are proved via stochastic means, whereas our uniqueness (comparison) results adapt techniques from viscosity solution theory. This paper, to our knowledge is the first treating rigorously impulse control for jump-diffusion processes in a general viscosity solution framework; the jump part may have infinite activity. In the proofs, no prior continuity of the value function is assumed, quadratic costs are allowed, and elliptic and parabolic results are presented for solutions possibly unbounded at infinity.

Subfields: Applied Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/07b4e65985c892cd652c6ad9567c0a417b936fd8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

  1. Peter A. Forsyth
  2. Y. Huang

In Control and Systems Engineering

  1. Peter A. Forsyth
  2. Y. Huang

In Finance

  1. Y. Huang
  2. Peter A. Forsyth
  3. Kenneth R. Vetzal
  4. Alexander Schied
  5. Jari Toivanen
  6. Samuli Ikonen
  7. S. Clift
  8. George Labahn

Citations in the corpus