Combined accumulation- and decumulation-plans with risk-controlled capital protection

Albrecht, Peter ; Weber, Carsten

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URN: urn:nbn:de:bsz:180-madoc-27749
Document Type: Working paper
Year of publication: 2003
The title of a journal, publication series: Rationalitätskonzepte, Entscheidungsverhalten und ökonomische Modellierung
Volume: 03-09
Place of publication: Mannheim
Publication language: English
Institution: School of Law and Economics > Sonstige - Fakultät für Rechtswissenschaft und Volkswirtschaftslehre
MADOC publication series: Sonderforschungsbereich 504 > Rationalitätskonzepte, Entscheidungsverhalten und ökonomische Modellierung (Laufzeit 1997 - 2008)
Subject: 330 Economics
Subject headings (SWD): Portfoliomanagement , Investmentfonds , Geldmarktfonds , Value at Risk
Keywords (English): Financial engineering , value-at-risk , capital protected accumulation plans
Abstract: We base our analysis on an investor, usually a retiree, endowed with a certain amount of wealth W, who considers both his own consumption needs (fixed periodic withdrawals) and the requirement of his heirs (defined bequest). For this purpose he pursues the following in-vestment strategy. The part F is invested in a set of investment funds with the target to achieve an accumulated wealth at the end of a certain time horizon of at least the original amount of wealth W (or the fraction ), measured in real terms. As certain investment risks are implied, we allow for the probability of falling short of the target and implement it into our model as a risk control parameter. The remaining part MM of the original wealth is invested in money market funds in order to avoid additional investment risks and deliver fixed periodic withdrawals until the end of the respective time horizon. The optimal investment strategy is the investment fund allocation that satisfies the probability of shortfall and mini-mizes F, while maximizing the fixed periodic withdrawals. We outline this investment prob-lem in a mathematical model and illustrate the solution for a reasonable choice of empirical parameters.

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