Age-Based Pension Payment Modeling Strategies

We propose a novel general framework to solve the optimal life-cycle investment strategy in pension funds, e.g., target date funds. We present two types of semi-adapted investment strategies, which are uniquely determined by the fund balance and the investor's current age. The key to our approach is a novel conditioning technique combined with calculus of variations techniques. For the most general case, we obtain semi-closed-form solutions subject to solving only one implicit equation. This approach does not impose the requirement of concavity on the utility function, hence we are able to extend the current literature on optimal pension investment to include cumulative prospect theory (CPT) preferences. The one-fund theorem remains valid under this strategy, which also yields the corresponding efficient frontier suitable for practical interpretations. Additionally, the unified framework can handle practical extensions such as portfolio constraints based on risk measures.

Jeff retired at 60 with £500,000 but he had one big problem… Jeff had worked hard for 40 years and was finally ready to enjoy retirement. ✔️ £500,000 in pensions & savings ✔️ No mortgage ✔️ Plans to travel, play golf, and spend time with family But when he sat down to plan his finances, one big question loomed over him… Would his money last? Jeff planned to withdraw £30,000 per year from his pension. That seemed reasonable—until he looked at the impact of: ⚠️ Inflation – £30,000 today won’t buy the same lifestyle in 20 years ⚠️ Market downturns – A few bad years could reduce his pot faster than expected ⚠️ Living longer than planned – What if he lived to 90+? Would he still have enough? At that rate, his pension could run out in his mid-80s, just when he might need it most for care costs or extra support. How Jeff fixed it (using Cashflow Modelling) Instead of guessing, Jeff worked with a financial planner who used cashflow modelling to map out his retirement finances. Here’s what it showed him: 📊 If he withdrew £30,000 per year without a strategy, his money could run out by age 83 📊 If he adjusted withdrawals, invested wisely & minimised tax, he could have enough until 95+ With a clear picture of how long his money could last, Jeff made smart changes: ✅ Adjusted his withdrawal strategy – Taking a flexible approach rather than a fixed amount each year ✅ Maximised tax efficiency – Withdrawing from different pots to reduce unnecessary tax ✅ Kept part of his pension invested – Allowing his money to grow even in retirement ✅ Planned for later-life costs – Factoring in potential care expenses so he wouldn’t be caught off guard Now, instead of worrying about running out, Jeff has a long-term plan based on real numbers… giving him peace of mind and the freedom to enjoy retirement. Key lesson… A big pension pot doesn’t always mean financial security. Without a clear plan, it’s easy to: 🚨 Withdraw too much, too soon 🚨 Pay more tax than necessary 🚨 Run out of money later in life Cashflow modelling helps you see the bigger picture, so you can make confident financial decisions for retirement 🙌