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 inter-ested 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 mea-sure 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 theoreti-cal results. Our strategy is also shown to yield a better distribution of the terminal wealth than traditional hedging approaches. & COPY; 2022 Elsevier B.V. All rights reserved.

Automated summary

In this paper, the authors derive constrained optimal investment strategies for long-term savers who want to invest in stocks but fear potential losses, such as their retirement income. The strategies, called probability hedging, can be derived under different utility functions and multifactor model assumptions. The authors demonstrate that the choice of utility function affects the probability measure and that logarithmic utility results in an intuitive probability hedge. This strategy not only facilitates communication but also provides a better distribution of terminal wealth compared to traditional hedging approaches.