The Finite Horizon Optimal Multi-Modes Switching Problem: the Viscosity Solution Approach
Brahim El Asri, Said Hamadene
TL;DR
This paper establishes the existence and uniqueness of solutions for a system of interconnected variational inequalities related to optimal multi-modes switching, with applications in financial firm valuation.
Contribution
It introduces a viscosity solution approach to a deterministic version of the Markovian optimal switching problem with arbitrary costs.
Findings
Proves existence and uniqueness of solutions.
Connects the problem to financial firm valuation.
Provides a mathematical framework for multi-modes switching.
Abstract
In this paper we show existence and uniqueness of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. This system is the deterministic version of the Verification Theorem of the Markovian optimal m-states switching problem. The switching cost functions are arbitrary. This problem is in relation with the valuation of firms in a financial market.
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Taxonomy
TopicsEconomic theories and models · Stochastic processes and financial applications