Optimal investment policies for a firm with a random risk process: Exponential utility and minimizing the probability of ruin

Optimal investment policies for a firm with a random risk process: Exponential utility and minimizing the probability of ruin

0.00 Avg rating0 Votes
Article ID: iaor20041476
Country: United States
Volume: 20
Issue: 4
Start Page Number: 937
End Page Number: 958
Publication Date: Nov 1995
Journal: Mathematics of Operations Research
Authors:
Keywords: risk, markov processes
Abstract:

We consider a firm that is faced with an uncontrollable stochastic cash flow, or random risk process. There is one investment opportunity, a risky stock, and we study the optimal investment decision for such firms. There is a fundamental incompleteness in the market, in that the risk to the investor of going bankrupt cannot be eliminated under any investment strategy, since the random risk process ensures that there is always a positive probability of ruin (bankruptcy). We therefore focus on obtaining investment strategies which are optimal in the sense of minimizing the risk of ruin. In particular, we solve for the strategy that maximizes the probability of achieving a given upper wealth level before hitting a given lower level. This policy also minimizes the probability of ruin. We prove that when there is no risk-free interest rate, this policy is equivalent to the policy that maximizes utility for terminal wealth, for a fixed terminal time, when the firm has an exponential utility function. This validates a longstanding conjecture about the relation between minimizing probability of ruin and exponential utility. When there is a positive risk-free interest rate, the conjecture is shown to be false. We also solve for the optimal policy for the related objective of minimizing the expected discounted penalty paid upon ruin.

Reviews

Required fields are marked *. Your email address will not be published.