Misuse and optimum inspecting strategy in agency problems

Assets misuse by an agent and the optimal audit inspecting strategy are analyzed in this paper. The agent and the principal are acting to maximize their expected utility and both are characterized by risk aversion. The agent’s decision about a theft takes into account the probability of benefiting from the stolen assets but also the probability of being penalized if caught. The principal’s decision about the optimal number of audit teams, hence, the probability of uncovering the theft, takes into account the cost involved, the probability of one team of auditors uncovering the theft and the agent’s decision about the theft. We get two response curves which describe the optimal behavior of both the agent and the principal and show that there may be a Nash solution to the problem. Since in real life there are often many principals (shareholders) with different utility functions, a set of efficient strategies is offered using the First and Second degree Stochastic Dominance rules. A numerical illustration which clarifies the methodology and displays the applicability of the model is also provided.