Target-Bequest Investment and Insurance Fund

Virginia R. Young

North American Actuarial Journal, 2018, vol. 22, issue 2, 182-197

Abstract: We propose a new type of investment fund, a Target-Bequest Fund (TBF), for which the manager of the fund invests to maximize the probability of reaching a bequest goal, specified by the investor. We assume the fund pays dividends at a rate proportional to the value of the fund, with the proportion also specified by the investor. In addition to considering this basic fund, we propose two extensions. The first extension is to impose a no-borrowing constraint. Indeed, unless the investment fund is a hedge fund, it will likely not allow the manager to invest more in the risky asset than is available in the fund, so this constraint is a realistic one. The second extension is to allow the fund manager to buy life insurance to help reach the bequest goal. We consider both extensions in the special case for which the proportional dividend rate is less than or equal to the riskless rate of return. Our focus is to obtain explicit solutions in a simplified market and insurance setting to give actuaries implementing this fund design some rules-of-thumb for investing in a financial market and buying life insurance in more realistic settings. We fully expect these rules-of-thumb to be generally valid in those more realistic settings.

Date: 2018
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DOI: 10.1080/10920277.2017.1381030

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