Optimal contracting under mean-volatility joint ambiguity uncertainties

Sung, Jaeyoung

doi:10.1007/s00199-021-01362-9

Cited by 15 publications

(4 citation statements)

References 45 publications

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“…This was also the conclusion of Carroll (2015) in a two-stage time-consistent model in which the principal demands robustness, in the sense of evaluating admissible contracts by their worst-case performance, over unknown actions the agent might take. Similar results we obtained by Sung (2005Sung ( , 2021 and Mastrolia and Possamaï (2018) in the continuous-time setting. Moreover, the results in Abi Jaber and Villeneuve (2023) show that the optimal contract remains linear when the output is driven by a Gaussian Volterra process (instead of Brownian motion).…”

Section: Results Examples and Qualitative Implicationssupporting

confidence: 89%

“…Following upon Holmström and Milgrom (1987), Sung (1993, 1997) studied the validity of the so-called first-order approach, while Sung (1995Sung ( , 1997 provided extensions to the case of diffusion control and hierarchical structures. The linearity of the optimal contract, a feature also present in Sung (1995), is further studied in Müller (1998Müller ( , 2000, Hellwig and Schmidt (2002), Hellwig (2007), and Sung (2005Sung ( , 2021 for the first-best problem, the interplay between the discrete-time and continuoustime models, and for a robust setting, respectively. Notably, Williams (2015) and Cvitanić et al (2009) characterize the optimal contract for general utilities by means of the so-called stochastic maximum principle and forward-backward stochastic differential equations (FBSDEs for short) 1 .…”

Section: Introductionmentioning

confidence: 99%

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Time‐inconsistent contract theory

Hernández,

Possamaï

2023

Mathematical Finance

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This paper investigates the moral hazard problem in finite horizon with both continuous and lump‐sum payments, involving a time‐inconsistent sophisticated agent and a standard utility maximizer principal: Building upon the so‐called dynamic programming approach in Cvitanić et al. (2018) and the recently available results in Hernández and Possamaï (2023), we present a methodology that covers the previous contracting problem. Our main contribution consists of a characterization of the moral hazard problem faced by the principal. In particular, it shows that under relatively mild technical conditions on the data of the problem, the supremum of the principal's expected utility over a smaller restricted family of contracts is equal to the supremum over all feasible contracts. Nevertheless, this characterization yields, as far as we know, a novel class of control problems that involve the control of a forward Volterra equation via Volterra‐type controls, and infinite‐dimensional stochastic target constraints. Despite the inherent challenges associated with such a problem, we study the solution under three different specifications of utility functions for both the agent and the principal, and draw qualitative implications from the form of the optimal contract. The general case remains the subject of future research. We illustrate some of our results in the context of a project selection contracting problem between an investor and a time‐inconsistent manager.

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Section: Results Examples and Qualitative Implicationssupporting

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Time‐inconsistent contract theory

Hernández,

Possamaï

2023

Mathematical Finance

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“…The weak formulation of SZSDGs and SDGs with random coefficients was considered in [10,11], where the existence of the open-loop type saddle point (Nash) equilibrium as well as the game value was established. Note also that SZSDGs and non-zero-sum stochastic differential games (SDGs) have been studied in several different directions, including the minimax solution approach [18], the characterization of multiple Nash equilibriums [19], the choice of the associated probability measure [20], the optimal contracting problem [21], the risk-sensitive SZSDG [22], the SZSDG with delay [23], and the SZSDG on the probability space [24]. Regarding some other recent processes and applications of SDGs, see [25,26] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

State and Control Path-Dependent Stochastic Zero-Sum Differential Games: Viscosity Solutions of Path-Dependent Hamilton–Jacobi–Isaacs Equations

Moon¹

2022

Mathematics

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In this paper, we consider the two-player state and control path-dependent stochastic zero-sum differential game. In our problem setup, the state process, which is controlled by the players, is dependent on (current and past) paths of state and control processes of the players. Furthermore, the running cost of the objective functional depends on both state and control paths of the players. We use the notion of non-anticipative strategies to define lower and upper value functionals of the game, where unlike the existing literature, these value functions are dependent on the initial states and control paths of the players. In the first main result of this paper, we prove that the (lower and upper) value functionals satisfy the dynamic programming principle (DPP), for which unlike the existing literature, the Skorohod metric is necessary to maintain the separability of càdlàg (state and control) spaces. We introduce the lower and upper Hamilton–Jacobi–Isaacs (HJI) equations from the DPP, which correspond to the state and control path-dependent nonlinear second-order partial differential equations. In the second main result of this paper, we show that by using the functional Itô calculus, the lower and upper value functionals are viscosity solutions of (lower and upper) state and control path-dependent HJI equations, where the notion of viscosity solutions is defined on a compact κ-Hölder space to use several important estimates and to guarantee the existence of minimum and maximum points between the (lower and upper) value functionals and the test functions. Based on these two main results, we also show that the Isaacs condition and the uniqueness of viscosity solutions imply the existence of the game value. Finally, we prove the uniqueness of classical solutions for the (state path-dependent) HJI equations in the state path-dependent case, where its proof requires establishing an equivalent classical solution structure as well as an appropriate contradiction argument.

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“…Li et al (2022) also show that the commitment against future debt dilution could be suboptimal because of inefficient ambiguity sharing. Sung (2022) analyzes a continuous-time principal-agent problem under ambiguity about both the mean and the volatility of a diffusion process. Both the principal and the agent have ambiguity-averse preferences represented by the utility model of Chen and Epstein (2002).…”

mentioning

confidence: 99%

Introduction to the special issue in honor of Larry Epstein

Miao

2022

Econ Theory

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He was elected a Fellow of the Econometric Society in 1989, an Economic Theory Fellow of the Society for the Advancement of Economicy Theory in 2011, and a Member of the American Academy of Arts and Science in 2013, and was awarded the Frisch Medal in 1994.Epstein has made numerous fundamental contributions in microeconomics, decision theory, and mathematical economics. His main research topics focus on how to model individual decision-making under uncertainty. He often adopts an axiomatic approach in abstract models, though always with an eye towards tractability and usefulness for applications, both theoretical and empirical. Besides applications within economics, his work has connections to finance (theoretical and empirical asset pricing), operations research (robust stochastic optimization), probability theory (limit theorems), and statistics (robust inference and hypothesis testing).This special issue contains ten papers contributed by Epstein's former students, coauthors, and fans. These papers are inspired and influenced by Epstein's research. Let me start with the papers related to Epstein's work on ambiguity.Halevy and Ozdenoren (2022) present a theoretical model of decision making in which preferences are defined on both Savage subjective acts and compound objective lotteries. They introduce the concept of two-stage probabilistically sophistication (2SPS), which generalizes the concept of probabilistically sophistication of Machina and Schmeidler (1992). The latter is used as a benchmark for ambiguity neutrality by Epstein (1999). Preferences are 2SPS when the ranking of acts corresponds to a ranking of the respective compound lotteries induced by the acts through the decision maker's subjective belief. This family of preferences includes various theoretical models (e.g., the smooth ambiguity model of Klibanoff et al. (2005)) that have been proposed in the literature to accommodate non-neutral attitude towards ambiguity. The principle B Jianjun Miao

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Optimal contracting under mean-volatility joint ambiguity uncertainties

Cited by 15 publications

References 45 publications

Time‐inconsistent contract theory

Time‐inconsistent contract theory

State and Control Path-Dependent Stochastic Zero-Sum Differential Games: Viscosity Solutions of Path-Dependent Hamilton–Jacobi–Isaacs Equations

Introduction to the special issue in honor of Larry Epstein

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