Portfolio insurance strategies that ensure a certain minimum portfolio value or floor such as the Constant Proportion Portfolio Insurance (CPPI) and the Option-based Portfolio Insurance are economically important and widely spread among the banking and insurance industries. In distress and volatile market environments, investors such as pension funds have a need to insure their portfolios against downside risk in order to meet certain future payments or liabilities. Non-anticipated shocks or negative interest rates, jumps, crashes, or overnight trading restrictions in stock prices could drop pension fund portfolios below desired levels (present value of pension obligations) making them underfunded with pension assets to pension liabilities ratio below 100%. In particular, within the current low interest rate environment, a high number of pension funds happen to be underfunded which is a severe practical problem. Because of such scenarios, there is a need for an investment strategy which covers both the case of funded and underfunded portfolios. This article introduces a novel strategy which generalizes the CPPI approach. It has the overall target of guaranteeing the investment goal or floor while participating in the performance of the assets and limiting the downside risk of the portfolio at the same time. We show that the strategy accounts for behavioral aspects of the investor such as distorted probabilities, a risk-averse behavior for gains, and a risk-seeking behavior for losses. The proposed strategy turns out to be optimal within the Cumulative Prospect Theory framework by Tversky and Kahneman (J Risk Uncertain 5(4):297–323, 1992).

中文翻译：

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行为投资组合保险策略

确保一定的最低投资组合价值或底线的投资组合保险策略，如恒定比例投资组合保险 (CPPI) 和基于期权的投资组合保险，在经济上很重要，并在银行和保险行业中广泛传播。在困境和动荡的市场环境中，养老基金等投资者需要确保其投资组合免受下行风险，以应对某些未来的付款或负债。非预期的冲击或负利率、跳涨、崩盘或股票价格的隔夜交易限制可能会使养老基金投资组合低于预期水平（养老金义务的现值），使其资金不足，养老金资产与养老金负债的比率低于 100%。尤其是在当前的低利率环境下，大量养老基金恰好资金不足，这是一个严重的实际问题。由于这种情况，需要一种涵盖资金充足和资金不足的投资组合情况的投资策略。本文介绍了一种概括 CPPI 方法的新策略。它的总体目标是在参与资产表现的同时保证投资目标或下限，同时限制投资组合的下行风险。我们表明该策略考虑了投资者的行为方面，例如扭曲的概率、收益的风险规避行为和损失的风险寻求行为。在 Tversky 和 ​​Kahneman (J Risk Uncertain 5(4):297–323, 1992) 的累积前景理论框架内，所提议的策略被证明是最佳的。