Multidimensional quadratic BSDEs with separated generators

Jamneshan, Asgar; Kupper, Michael; Luo, Peng

doi:10.1214/17-ecp87

Cited by 24 publications

(21 citation statements)

References 22 publications

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“…Their applications can be found in [2] and [26]. Recently, there have been a renewed interest in the corresponding quadratic BSDE systems due to their various applications in equilibrium problems, price impact models and non-zero sum games (see, for example, [11,30,31,34,35,45] with more references therein). In spite of all the aforementioned results, our paper seems to be the first to introduce and solve quadratic BSDE systems in an infinite time horizon.…”

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confidence: 99%

Systems of Ergodic BSDEs Arising in Regime Switching Forward Performance Processes

Hu¹,

Liang²,

Tang³

2020

SIAM J. Control Optim.

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We introduce and solve a new type of quadratic backward stochastic differential equation systems defined in an infinite time horizon, called ergodic BSDE systems. Such systems arise naturally as candidate solutions to characterize forward performance processes and their associated optimal trading strategies in a regime switching market. In addition, we develop a connection between the solution of the ergodic BSDE system and the long-term growth rate of classical utility maximization problems, and use the ergodic BSDE system to study the large time behavior of PDE systems with quadratic growth Hamiltonians.

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confidence: 99%

Systems of Ergodic BSDEs Arising in Regime Switching Forward Performance Processes

Hu¹,

Liang²,

Tang³

2020

SIAM J. Control Optim.

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“…Based on the works of [Esp10] and [ET15], the authors of [FDR11] give several counter examples to the existence of solutions; nonetheless, positive results do exist although none are very general, see e.g. [Tev08], [CN15], [Fre14], [KP16], [HT16], [XŽ16], [JKL14] and [LT15]. In our case we are able to solve the system.…”

Section: Introductionmentioning

confidence: 69%

Equilibrium Pricing Under Relative Performance Concerns

Bielagk¹,

Lionnet²,

Reis³

2017

SIAM J. Finan. Math.

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We investigate the effects of the social interactions of a finite set of agents on an equilibrium pricing mechanism. A derivative written on non-tradable underlyings is introduced to the market and priced in an equilibrium framework by agents who assess risk using convex dynamic risk measures expressed by Backward Stochastic Differential Equations (BSDE). Each agent is not only exposed to financial and non-financial risk factors, but she also faces performance concerns with respect to the other agents.Within our proposed model we prove the existence and uniqueness of an equilibrium whose analysis involves systems of fully coupled multi-dimensional quadratic BSDEs. We extend the theory of the representative agent by showing that a non-standard aggregation of risk measures is possible via weighted-dilated infimal convolution. We analyze the impact of the problem's parameters on the pricing mechanism, in particular how the agents' performance concern rates affect prices and risk perceptions. In extreme situations, we find that the concern rates destroy the equilibrium while the risk measures themselves remain stable.

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“…Motivated by recent developments of solvability of multi-dimesional quadratic BSDEs (see [16,6,7,13,3,18]), we consider multi-dimensional RBSDEs with diagonally quadratic generators. By a standard technique, we introcude the penalized BSDEs and provide some delicated a priori estimates for their solutions.…”

Section: Introductionmentioning

confidence: 99%