On an asymptotic viscosity solution property of solutions of discrete Hamilton–Jacobi–Bellman equations

Journal Article · Sun Jul 15 00:00:00 EDT 2018 · Computational and Applied Mathematics

DOI:https://doi.org/10.1007/S40314-017-0549-3· OSTI ID:22769254

Yoshida, Naohiro ^[1]

---

1. Hitotsubashi University, Graduate School of Economics (Japan)

In this paper, we show that a proper limit of solutions of discrete Hamilton–Jacobi–Bellman (dHJB) equations in a random walk model becomes a viscosity solution of a Hamilton–Jacobi–Bellman (HJB) variational inequality in a continuous-time geometric Brownian model. HJB variational inequalities are used to analyze singular stochastic control problems in mathematical finance. By our result, with the help of dHJB equations, we can obtain viscosity solutions of HJB variational inequalities which are usually identified with the value functions of the singular stochastic control problems.

• OSTI ID: 22769254
• Journal Information: Computational and Applied Mathematics, Vol. 37, Issue 3; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); ISSN 0101-8205
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
ASYMPTOTIC SOLUTIONS
EQUATIONS
GRAPH THEORY
RANDOMNESS
STOCHASTIC PROCESSES
VARIATIONAL METHODS
VISCOSITY