Application of the calculus of variations to financing alternatives

The problem considered is to choose from a finite set of inter-related investment and financing alternatives and also levels of consumption/work over time in order to maximise a utility functional. Each investment and financing option is characterised by its cash flow over time. An inter-temporal budget requirement operates continuously. Application of Calculus of Variations leads to consideration of the Euler-Lagrange equations combined with Kulm-Tucker conditions. It is shown that the solution (also when there are logical dependencies present) requires the maximisation of a Generalised Net Present Wealth measure in which the discount factor is formed from an integral of the Lagrangean multiplier function.financial investment calculus of variations Lagrange multipliers net present value