• Mingliang Cheng

Student thesis: Phd


We investigate the impact of cash reserves upon the optimal behaviour of a modelled firm that has uncertain future revenues. To achieve this, we build up a corporate financing model of a firm from a Real Options foundation, with the option to close as a core business decision maintained throughout. We model the firm by employing an optimal stochastic control mathematical approach, which is based upon a partial differential equations perspective. In so doing, we are able to assess the incremental impacts upon the optimal operation of the cash constrained firm, by sequentially including: an optimal dividend distribution; optimal equity financing; and optimal debt financing (conducted in a novel equilibrium setting between firm and creditor). We present efficient numerical schemes to solve these models, which are generally built from the Projected Successive Over Relaxation (PSOR) method, and the Semi-Lagrangian approach. Using these numerical tools, and our gained economic insights, we then allow the firm the option to also expand the operation, so they may also take advantage of favourable economic conditions.
Date of Award1 Aug 2016
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorGeoffrey Evatt (Supervisor) & Paul Johnson (Supervisor)


  • Semi-Lagrangian Methods
  • Optimal Dividends
  • Optimal Investment
  • Stochastic Control
  • Real Options
  • Corporate Finance
  • Debt Financing

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