A probability of ruin approach to optimize pension fund investments Abraham Hern ´ andez-Pacheco 1 ,2 , Agnieszka I. Bergel 1 , Alfredo D. Eg´ ıdio dos Reis 1 1 ISEG & CEMAPRE, Universidade de Lisboa; 2 VITALIS abe@vitalis.com.mx, agnieszka@iseg.ulisboa.pt, alfredo@iseg.ulisboa.pt Abstract We use a novel concept of ruin probabilities to optimize the asset allocation for var- ious asset classes in a pension fund. We look at a sponsor of a Defined Benefit plan, where current assets plus the expected present value of future contributions are smaller than the expected present value of its liabilities discounted at a ”risk free” interest rate; such is the case of thousands of pension plans worth trillions of $USD. This is proposal is an alternative to the Solvency II framework. We present an alternative methodology to classical Asset Liability Management tech- niques that consider the long-term effects of returns versus volatility, along with funding levels and funding policy. For several combinations of asset allocation, as well as a proper concept and definition of a ”ruin probability”, our approach estimates the port- folio’s probability of ruin. We particularly study the asset allocation of a portfolio that minimizes the probability of reaching a threshold where there is the need to increase contributions or curtail benefits (our ruin concept), under a set of different assumptions of initial funding, future contributions, and financial forecasting models. We will call such portfolio the Minimum Ruin Probability (MRP) portfolio. Our project also comes as sequel and development of the paper by Hern´ andez- Pacheco and Salgado (2015). We explain the idea and rationale of using the probability of ruin to optimize asset allocation, its relation with other optimization techniques and novel empirical preliminary results. 1 Introduction According to OCDE (2020), pension funds and retirement assets exceeded 32 trillion $USD by 2019, just in the OECD countries. Today this figure may have changed to closer to $40 trillion, almost 1/2 of world GDP. In the past ten years, investment returns have been twice the amount of sponsor’s con- tributions to defined benefit plans in the U.S. (with information from the U.S. DOL (2021)). During the same period, average stock market returns have been 14% while Treasury Bills returns have been 3.6% (according to data from NYU (2021)). Thus, arguably the most im- portant decision for a pension plan sponsor is the asset allocation of the pension fund. First author has worked for 30 years as a pension actuary and asset manager for pension funds and has indeed experienced that, quoting Sherris (1993), ”variation in asset values is ar- guably the most significant component in the determination of the probability of ruin of pension funds”. 1