Optimal investment strategies for participating contracts

Lin, Hongcan; Saunders, David; Weng, Chengguo

doi:10.1016/j.insmatheco.2017.02.001

Cited by 25 publications

(12 citation statements)

References 24 publications

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“…K * (t) and K * * (t) are the discounted values of these two thresholds, that means that for X(t) > K * * (t) the asset manager can always beat the minimum guarantee by investing all the AUM at the risk free rate, instead for X(t) > K * (t) the asset manager can always reach a positive wealth. The strategy is similar to the one derived in [14], the main difference is that as they allow for a negative remuneration the no-investment region is not observed, i.e., in their setting K * (t) = 0, and the hump shaped part starts at X(t) = 0.…”

Section: Numerical Analysismentioning

confidence: 92%

“…In a recent article [14], the problem has been analyzed in a constant interest rate setting assuming that the AUM can go below the guarantee threshold, and considering the perspective of the asset manager of the insurance company, see also [11] for an analysis of a manager of a hedge fund. In these two articles, authors assume that the asset manager takes the whole loss in case the guarantee is not reached, if this is the case then her remuneration may even become negative.…”

Section: Introductionmentioning

confidence: 99%

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Optimal investment strategies with a minimum performance constraint

2019

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We consider the optimal investment problem of a fund manager in the presence of a minimum guarantee constraint on the fund performance. The manager receives a fee which is proportional to the liquidation value of the portfolio or of the surplus over the guarantee in case it is positive and zero otherwise, eventually augmented by a constant fee. Her remuneration is reduced through the application of a penalty if the value of the fund at maturity is below a specified-in-advance threshold (minimum guarantee). We deal with two different settings: a continuous time economy with constant instantaneous interest rate and the case where the short-term interest rate evolves as the Vasicek model. Explicit formulas for the optimal investment strategy are presented. We compare our portfolio strategies to the Merton portfolio and to the Option Based Portfolio Insurance strategy.JEL Classification: C61, G11, G23

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Section: Numerical Analysismentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Optimal investment strategies with a minimum performance constraint

2019

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“…Context RA RS LA First-order RA Merton (1969) CRRA and CARA Carpenter (2000) Option payoff with HARA utilities Berkelaar, Kouwenberg and Post (2004) Loss aversion case Berkelaar, Kouwenberg and Post (2004) Kinked power utility case Lin, Saunders and Weng (2017) Participating insurance contracts He and Kou (2018) First-Loss schemes in hedge funds He, Liang, Liu and Ma (2019) Incentive schemes in pension funds Liang and Liu (2019) Central-planned portfolio selection Liang and Liu (2020) Principal's constraint…”

Section: Literaturementioning

confidence: 99%

“…On its whole domain, the utility may not be concave, differentiable or continuous. The family comes from the following practical aspects: (1) the basic HARA utility (e.g., Merton (1969Merton ( , 1971)); (2) in many decision-based areas (e.g., hedge fund management), the actual utility/objective function is the composition of the HARA preference and piecewise linear payoff (e.g., Carpenter (2000); Berkelaar, Kouwenberg and Post (2004); He, Liang, Liu and Ma (2019)); (3) some non-concave utilities in behavioral settings (e.g., Kouwenberg and Ziemba (2007); Lin, Saunders and Weng (2017); He and Kou (2018); Liang and Liu (2019)). Nevertheless, the extensive literature solve the optimization problem and express the optimal portfolio in different closed forms.…”

Section: Introductionmentioning

confidence: 99%

A Unified Formula of the Optimal Portfolio for Piecewise Hyperbolic Absolute Risk Aversion Utilities

Liang¹,

Liu²,

Ma³

2021

Preprint

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We propose a general family of piecewise hyperbolic absolute risk aversion (PHARA) utility, including many non-standard utilities as examples. A typical application is the composition of an HARA preference and a piecewise linear payoff in hedge fund management. We derive a unified closed-form formula of the optimal portfolio, which is a four-term division. The formula has clear economic meanings, reflecting the behavior of risk aversion, risk seeking, loss aversion and first-order risk aversion. One main finding is that risk-taking behaviors are greatly increased by non-concavity and reduced by non-differentiability.

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“…Closer to the mentioned literature in the more specific surplus setting [17,20], the work of [12] investigates how different surplus distribution mechanisms affect the risk exposure of life insurance companies that sell performance-participating life insurance contracts. [15] obtain closed-form solutions for optimal investment strategies with performance-participating liabilities in a complete market for S-shaped utility functions. By optimizing the terminal surplus in the presence of index-and performance-linked liabilities, which might include unhedgeable risks as well, our paper establishes a link between the literature on portfolio optimization with stochastic liabilities and the literature on insurance products.…”

Section: Introductionmentioning

confidence: 99%

Dynamic surplus optimization with performance- and index-linked liabilities

2021

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The increasing importance of liability-driven investment strategies and the shift towards retirement products with lower guarantees and more performance participation provide challenges for the development of portfolio optimization frameworks which cover these aspects. To this end, we establish a general and flexible terminal surplus optimization framework in continuous time, allowing for dynamic investment strategies and stochastic liabilities, which can be linked to the performance of an index or the asset portfolio of the insurance company. Besides optimality results in a fairly general surplus optimization setting, we obtain closed-form solutions for the optimal investment strategy for various specific liability models, which include the cases of index-linked and performance-linked liabilities and liabilities which are completely or only partially hedgeable. We compare the results in numerical examples and study the impact of the performance participation, unhedgeable risk components, different ways of modeling the liabilities and the relative risk aversion parameter. We find that performance- or index-linked liabilities, which provide a close link between the wealth of the insurance company and its liabilities, allow for a higher allocation in the risky investment. On the other hand, unhedgeable risks reduce the allocation in the risky investment. We conclude that, aiming at a high expected return for the policy holder, insurance companies should try to connect the performance of insurance products closely to the wealth and minimize unhedgeable risks.

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Optimal investment strategies for participating contracts

Cited by 25 publications

References 24 publications

Optimal investment strategies with a minimum performance constraint

Optimal investment strategies with a minimum performance constraint

A Unified Formula of the Optimal Portfolio for Piecewise Hyperbolic Absolute Risk Aversion Utilities

Dynamic surplus optimization with performance- and index-linked liabilities

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