Capital Budgeting Problems: A Parameterized Point of View

Abstract

A fundamental financial problem is budgeting. A firm is given a set of financial instruments $X=\{x_1,\ldots ,x_n\}$ over a number of time periods T. Every instrument $x_i$ has a return of $r_i$ and for time period $t=1,\ldots ,T$ a price of $p_{t,i}$. Further for every time period t there is budget $b_t$. The task is to choose a portfolio $X'$ from X such that for every time period $t=1,\ldots ,T$ the prices of the portfolio do not exceed the budget $b_t$ and the return of the portfolio is maximized. We study the fixed-parameter tractability of the problem. For a lot of small parameter values we obtain efficient solutions for the capital budgeting problem. We also consider the connection to pseudo-polynomial algorithms.