How suboptimal are linear sharing rules?

Jensen, Bjarne Astrup; Nielsen, J. Aase

doi:10.1007/s10436-016-0279-3

Cited by 15 publications

(8 citation statements)

References 24 publications

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“…Jensen and Nielsen (2016) consider a similar social planner whose sharing rule is initially fixed to be linear, though. Branger et al (2018a) consider a rather similar setting as Jensen and Nielsen (2016) but generalize the analysis to n investors instead of two.…”

Section: Propositionmentioning

confidence: 99%

“…In addition, it can be shown that this linear sharing rule does not necessarily fulfill the financial fairness condition. It has been documented that this linear sharing rule is suboptimal, see, for example, Jensen and Nielsen (2016) and Branger et al (2018a). In our numerical analysis, we will quantify the possible utility loss for the individuals.…”

Section: Propositionmentioning

confidence: 99%

“…In other words, individual welfare does not deteriorate in both financial markets if an appropriate state-dependent sharing rule is applied. Under more prevailing sharing rules, like linear ones, this result holds no longer, as linear sharing rules impose a certain suboptimality to the collective [see, for example, Jensen and Nielsen (2016)]. Then, either all the individuals in the collective suffer a loss or an unfair distribution of the terminal wealth, where some individuals benefit at the cost of others, results.…”

Section: Introductionmentioning

confidence: 99%

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A collective investment problem in a stochastic volatility environment: The impact of sharing rules

Chen¹,

Nguyen

Rach³

2021

Ann Oper Res

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It is typical in collectively administered pension funds that employees delegate fund managers to invest their contributions. In addition, many pension funds still need to sustain guarantees (prescribed by law) in spite of the current low interest environment. In this paper, we consider an optimal collective investment problem for a pool of investors who (implicitly) demand minimum guarantees by deriving utility from the wealth exceeding their guarantees in two financial market settings, one with a stochastic and one with a constant volatility. We find that individual investors’ well-being will not be worsened through the collective investment in both financial markets, as individual optimal solutions are attainable if a financially fair state-dependent sharing rule is applied. When more prevailing sharing rules like linear rules are applied, this holds no longer. Furthermore, the degree of sub-optimality imposed by linear sharing rules is more pronounced in the stochastic volatility market than in the constant volatility market.

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Section: Propositionmentioning

confidence: 99%

Section: Propositionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A collective investment problem in a stochastic volatility environment: The impact of sharing rules

Chen¹,

Nguyen

Rach³

2021

Ann Oper Res

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“…Many of the more advanced problems studied in this literature such as sharing rules (e.g. Jensen and Nielsen, 2016;Branger et al, 2019) or generation effects (e.g. Schumacher, 2021) are beyond the scope of this paper.…”

Section: Introductionmentioning

confidence: 99%

Robust Decisions for Heterogeneous Agents via Certainty Equivalents

Balter¹,

Schweizer²

2021

Preprint

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We study the problem of a planner who resolves risk-return trade-offs -like financial investment decisions -on behalf of a collective of agents with heterogeneous risk preferences. The planner's objective is a two-stage utility functional where an outer utility function is applied to the distribution of the agents' certainty equivalents from a given decision. Assuming lognormal risks and heterogeneous power utility preferences for the agents, we characterize optimal behavior in a setting where the planner can let each agent choose between different options from a fixed menu of possible decisions, leading to a grouping of the agents by risk preferences. These optimal decision menus are derived first for the case where the planner knows the distribution of preferences exactly and then for a case where he faces uncertainty about this distribution, only having access to upper and lower bounds on agents' relative risk aversion. Finally, we provide tight bounds on the welfare loss from offering a finite menu of choices rather than fully personalized decisions. * We thank Antje Mahayni, Peter Schotman, Hans Schumacher and participants at the Netspar International Pension Workshop 2021 for very helpful comments and discussions.

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“…Papers on utility losses caused by (suboptimal) investment strategies include Jensen and Sørensen (2001), Jensen and Nielsen (2016) and Chen et al (2019). 5 Chen et al (2019) consider a general utility maximization under fair-pricing and budget constraints in a complete, arbitrage-free Black and Scholes model setup for an CRRA Investor.…”

Section: Introductionmentioning

confidence: 99%

Minimum return rate guarantees under default risk: optimal design of quantile guarantees

2020

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The paper analyzes the design of participating life insurance contracts with minimum return rate guarantees. Without default risk, the insured receives the maximum of a guaranteed rate and a participation in the investment returns. With default risk, the payoff is modified by a default put implying a compound option. We represent the yearly returns of the liabilities by a portfolio of plain vanilla options. In a Black and Scholes model, the optimal payoff constrained by a maximal shortfall probability can be stated in closed form. Due to the completeness of the market, it can be implemented for any equity to debt ratio. Keywords Guarantee scheme • Derivatives • Life insurance • Return rate guarantees • Default risk • Regulatory requirements • Utility to the insured JEL Classification G 31 • G 22 The authors gratefully acknowledge financial support by the German Insurance Science Association (DVfVW). In addition the authors would like to thank the two anonymous referees for their valuable and helpful suggestions and comments.

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How suboptimal are linear sharing rules?

Cited by 15 publications

References 24 publications

A collective investment problem in a stochastic volatility environment: The impact of sharing rules

A collective investment problem in a stochastic volatility environment: The impact of sharing rules

Robust Decisions for Heterogeneous Agents via Certainty Equivalents

Minimum return rate guarantees under default risk: optimal design of quantile guarantees

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