On Optimal Constrained Investment Strategies for Long-Term Savers in Stochastic Environments and Probability Hedging

In this paper, we derive constrained optimal investment strategies for long-term savers who are interested in investing their funds in stocks, but are afraid of potentially losing, for example, their retirement income. We call this probability hedging as it is determined by the probability of landing up within bounds that are agreed from interaction with the investor. We show that our strategies can be derived under different utility functions and multifactor model assumptions. We prove that the probability measure varies with the utility function choice and that the logarithmic utility, in particular, results in an intuitive probability hedge under the physical measure. This makes it easier to communicate, without putting at risk the financial advice conducted by potentially misrepresenting the realism of the theoretical results. Our strategy is also shown to yield a better distribution of the terminal wealth than traditional hedging approaches