The optimal solution to a principal-agent problem with unknown agent ability

Lai, Chong; Liu, Lishan; Li, Rui

doi:10.3934/jimo.2020084

Cited by 5 publications

(12 citation statements)

References 26 publications

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“…Three groups of studies were related to this work. Our study is related to the fast-growing literature that emphasizes information asymmetry in dynamic contracting problems (Giat and Subramanian, 2013;He et al, 2017;Lai et al, 2021). He et al (2017) extended the model of DeMarzo and Sannikov (2017) by introducing uncertainty and learning into a long-term contracting problem.…”

Section: Related Literaturementioning

confidence: 98%

“…Using the dynamic programming technique, they derived the optimal contract, which is contingent on the information rent that the principal rewards the agent. Lai et al (2021) investigated a principal-agent model featuring unknown agent's ability utilizing martingale and variational methods. They found that the agent's ability is completely revealed as the contractual duration tends to be infinite (long-term), and both the agent's payment and the principal's consumption depend on the agent's promised utility.…”

Section: Related Literaturementioning

confidence: 99%

“…They found that the agent's ability is completely revealed as the contractual duration tends to be infinite (long-term), and both the agent's payment and the principal's consumption depend on the agent's promised utility. Our study develops Lai et al (2021) by incorporating information asymmetry and adopting the discrete-time approximation theory of Hellwig and Schmidt (2002), and Biais et al (2007) to solve the continuous-time contracting model. The optimal contract we obtain is explicit and does not rely on any state variables.…”

Section: Related Literaturementioning

confidence: 99%

“…In reality, VCs often faces problems such as model uncertainty, information asymmetry, and behavior preference et al, which would increase the operational risk of the project. Recently, many scholars have considered the VC's risk aversion, such as Williams (2015), Cvitani c et al (2017), Trabelsi and Siyahhan (2021) and Lai et al (2021). Cvitani c et al…”

Section: Related Literaturementioning

confidence: 99%

“…They show that the optimal contract is linear in the contractible sources of risk, output, quadratic variation of output and crossvariation between output and contractible risk sources. Lai et al (2021) investigated a principal-agent model featured with the unknown agent ability. Under exponential utilities, we obtain the solutions of the optimal contracts that are explicitly contingent on the degree of risk aversion.…”

Section: Related Literaturementioning

confidence: 99%

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Optimal contracting with asymmetric belief and complementarity

Chang

Liu

2023

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PurposeIn this study, a dynamic contracting model is developed between a venture capitalist (VC) and an entrepreneur (EN) to explore the influence of asymmetric beliefs regarding output-relevant parameters, agency conflicts and complementarity on the VC's posterior beliefs through the EN's unobservable effort choices to influence the optimal dynamic contract.Design/methodology/approachThe authors construct the contracting model by incorporating the VC's effort, which is ignored in most studies. Using backward induction and a discrete-time approximation approach, the authors solve the continuous-time contract design problem, which evolves into a nonlinear ordinary differential equation (ODE).FindingsThe optimal equity share that the VC provides to the EN decreases over time. In accordance with the empirical evidence, the EN's optimistic beliefs regarding the project's profitability positively affect its equity share. However, the interactions between the optimal equity share, project risk and both partners' degrees of risk aversion are not monotonic. Moreover, the authors find that the optimal equity share increases with the degree of complementarity, which indicates that the EN is willing to cooperate with the VC. This study’s results also show that the optimal equity shares at each time are interdependent if the VC is risk-averse and independent if the VC is risk-neutral.Research limitations/implicationsIn conclusion, the authors highlight two potential directions for future research. First, the authors only considered a single VC, whereas in practice, a risk project may be carried out by multiple VCs, and it is interesting to discuss how the degree of complementarity affects the number of VCs that ENs contract. Second, the authors may introduce jumps and consider more general multivariate stochastic volatility models for output dynamics and analyze the characteristics of the optimal contracts. Third, further research can deal with other forms of discretionary output functions concerning complementarity, such as Cobb–Douglas and constant elasticity of substitution (See Varian, 1992).Social implicationsThe results of this study have several implications. First, it offers a novel approach to designing dynamic contracts that are specific and easy to operate. To improve the complicated venture investment situation and abate conflict between contractual parties, this study plays a good reference role. Second, the synergy effect proposed in this study provides a theoretical explanation for the executive compensation puzzle in economics, in which managers are often “rewarded for luck” (Bertrand and Mullainathan, 2001; Wu et al., 2018). This result indicates a realistic perspective on financing and establishing cooperative relationships, which enhances the efficiency of venture investment. Third, from an empirical standpoint, one can apply this framework to study research and development (R&D) problems.Originality/valueFirst, the authors introduce asymmetric beliefs and Bayesian learning to study the dynamic contract design problem and discuss their effects on equity share. Second, the authors incorporate the VC's effort into the contracting problem, and analyze the synergistic effect of effort complementarity on the optimal dynamic contract.

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Section: Related Literaturementioning

confidence: 98%

Section: Related Literaturementioning

confidence: 99%

Section: Related Literaturementioning

confidence: 99%

Section: Related Literaturementioning

confidence: 99%

Section: Related Literaturementioning

confidence: 99%

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Optimal contracting with asymmetric belief and complementarity

Chang

Liu

2023

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Agency theory: Forecasting agent remuneration at insurance companies

García¹,

Orozco²,

Pineda³

et al. 2023

Expert Systems with Applications

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Optimal contracting with asymmetric risk aversion information and fairness concerns

Chang,

Hu,

Zhao

2023

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PurposeThis study considers a contracting problem between a fairness concerned entrepreneur (EN) and a fair-neutral venture capitalist (VC) to explore the effects of asymmetry, agency conflicts and fairness concerns.Design/methodology/approachThe authors construct the model by assuming the EN's risk aversion degree is private information, which is more realistic but ignored in most studies. Under the principal–agent framework, the authors solve the VC's optimal contracting models by identifying the ranges of feasible solution, where the optimal solutions of these models are explicit and nicely reconcile the “private equity” puzzle. Moreover, validity of the optimal solutions is verified by numerical simulations.FindingsIn accordance with empirical evidence, information asymmetry lowers the optimal equity share that the VC provides to EN but raises EN's profit due to lower effort disutility and information rent. Moreover, the authors find that the fairness concerns is beneficial for the EN, where it not only increases the EN's optimal equity share, but also enhances the certainty equivalence of the EN's utility regarding its profit. Relative to the benchmark model where the EN's risk aversion degree is common knowledge, the EN's efforts recommended by the optimal contract is less sensitive to the EN's fairness concerns degree when the EN does not actually announce its risk aversion degree.Originality/valueFirst, the authors incorporate asymmetry to study a two-period contracting problem and explore how it affects the equity shares allocated to the contractual parties. Second, the authors incorporate fairness concerns and analyze its effect regarding the decision-makings and profits.

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The optimal solution to a principal-agent problem with unknown agent ability

Cited by 5 publications

References 26 publications

Optimal contracting with asymmetric belief and complementarity

Optimal contracting with asymmetric belief and complementarity

Agency theory: Forecasting agent remuneration at insurance companies

Optimal contracting with asymmetric risk aversion information and fairness concerns

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