Optimal entry to an irreversible investment plan with non convex costs

Angelis, Tiziano De; Ferrari, Giorgio; Martyr, Randall; Moriarty, John

doi:10.1007/s11579-017-0187-y

Cited by 1 publication

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“…For example, in the option pricing problem, the pricing model for American backdated options can be described as a two-dimensional free boundary problem [29][30][31]. De Angelis et al [32] considered the problem of optimal entry into an irreversible investment scheme with a cost function that is non-convex for the control variables, where it is necessary to study optimal entry policies with an irregular boundary. If the state space is irregular, the special handling of region interiors and boundaries is required, which may increase some computational complexity [33].…”

Section: Introductionmentioning

confidence: 99%

A Generalized Finite Difference Method for Solving Hamilton–Jacobi–Bellman Equations in Optimal Investment

Lin

Hoe

et al. 2023

Mathematics

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This paper studies the numerical algorithm of stochastic control problems in investment optimization. Investors choose the optimal investment to maximize the expected return under uncertainty. The optimality condition, the Hamilton–Jacobi–Bellman (HJB) equation, satisfied by the value function and obtained by the dynamic programming method, is a partial differential equation coupled with optimization. One of the major computational difficulties is the irregular boundary conditions presented in the HJB equation. In this paper, two mesh-free algorithms are proposed to solve two different cases of HJB equations with regular and irregular boundary conditions. The model of optimal investment under uncertainty developed by Abel is used to study the efficacy of the proposed algorithms. Extensive numerical studies are conducted to test the impact of the key parameters on the numerical efficacy. By comparing the numerical solution with the exact solution, the proposed numerical algorithms are validated.

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