Approximating the Growth Optimal Portfolio and Stock Price Bubbles

Platen, Eckhard; Rendek, Renata

doi:10.1142/s021902492050048x

Cited by 5 publications

(2 citation statements)

References 35 publications

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“…A similar comment applies to the choice of the S&P500 total return index as proxy for the numéraire portfolio or benchmark. Very likely, there exist better proxies for the numéraire portfolio, see for example Le & Platen (2006) or Platen & Rendek (2017). As will become clear, their larger long-term growth rates would make the effect to be demonstrated even more pronounced.…”

Section: Savings Bondmentioning

confidence: 99%

Less-expensive long-term annuities linked to mortality, cash and equity

Fergusson

Platen²

2022

Ann. actuar. sci.

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This paper proposes a shift in the valuation and production of long-term annuities, away from the classical risk-neutral methodology towards a methodology using the real-world probability measure. The proposed production method is applied to three examples of annuity products, one having annual payments linked to a mortality index and the savings account and the others having annual payments linked to a mortality index and an equity index with a guarantee that is linked to the same mortality index and the savings account. Out-of-sample hedge simulations demonstrate the effectiveness of the proposed less-expensive production method. In contrast to classical risk-neutral production, which revolves around the savings account as reference unit, the long-term best-performing portfolio, the numéraire portfolio of the equity market, is employed as the fundamental reference unit in the production of the annuity. The numéraire portfolio is the strictly positive, tradable portfolio that when used as denominator or benchmark makes all benchmarked non-negative portfolios supermartingales. Under real-world valuation, the initial benchmarked value of a benchmarked contingent claim equals its real-world conditional expectation. The proposed real-world valuation and production can lead to significantly lower values of long-term annuities and their less-expensive production than suggested by the risk-neutral approach.

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Section: Savings Bondmentioning

confidence: 99%

Less-expensive long-term annuities linked to mortality, cash and equity

Fergusson

Platen²

2022

Ann. actuar. sci.

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“…Empirical evidence, e.g. in [6, 7, 54, 63], and theoretical considerations, e.g. in [44, 49, 52], point out that the NFLVR condition may be too restrictive for realistic long-term modeling, and that there are less expensive ways of producing long-term payouts than widely practiced under the NFLVR condition, which is somehow equivalent to risk-neutral pricing and hedging.…”

Section: Introductionmentioning

confidence: 99%

No arbitrage and multiplicative special semimartingales

Platen

Tappe

2023

Adv. Appl. Probab.

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Consider a financial market with nonnegative semimartingales which does not need to have a numéraire. We are interested in the absence of arbitrage in the sense that no self-financing portfolio gives rise to arbitrage opportunities, where we are allowed to add a savings account to the market. We will prove that in this sense the market is free of arbitrage if and only if there exists an equivalent local martingale deflator which is a multiplicative special semimartingale. In this case, the additional savings account relates to the finite-variation part of the multiplicative decomposition of the deflator.

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Managing the shortfall risk of target date funds by overfunding

Barone Adesi,

Platen,

Sala

2024

Journal of Pension Economics and Finance

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Is it possible to achieve almost riskless, nonfluctuating investment payoffs in the long run, at a fraction of the traditional funding requirement, using equity investments? What is their shortfall risk? These questions are motivated by the need to increase yields, while limiting the variability of investment results. We show how to use contingent claims, denominated in units of a stock index, to achieve an almost riskless investment outcome. To control the risk of the proposed hedge portfolios, we introduce an overfunded scheme and show its reliability using bootstrapping. Results show that a modest amount of overfunding is an effective risk-management approach that brings the probability of not achieving the target to less than 1 percent. Our results are based on the use of the minimal market model and a change of numeraire. Robustness tests support their validity under different market specifications.

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Approximating the Growth Optimal Portfolio and Stock Price Bubbles

Cited by 5 publications

References 35 publications

Less-expensive long-term annuities linked to mortality, cash and equity

Less-expensive long-term annuities linked to mortality, cash and equity

No arbitrage and multiplicative special semimartingales

Managing the shortfall risk of target date funds by overfunding

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