An ergodic BSDE approach to forward entropic risk measures: representation and large-maturity behavior

Chong, Wing Fung; Hu, Ying; Liang, Gechun; Zariphopoulou, Thaleia

doi:10.1007/s00780-018-0377-3

Cited by 25 publications

(28 citation statements)

References 36 publications

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“…It bypasses a number of aforementioned difficulties inherited in the associated SPDE. See also [12] for a further development of this method to study forward entropic risk measures.…”

mentioning

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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“…It bypasses a number of aforementioned difficulties inherited in the associated SPDE. See also [12] for a further development of this method to study forward entropic risk measures.…”

mentioning

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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“…Note that ( 15) and ( 16) are the martingale characterization of the lower value of the game in (12), whereas ( 18) and ( 19) characterize the upper value of the game in (13).…”

Section: A Stochastic Differential Game Approachmentioning

confidence: 99%

“…The aim of this paper is to study optimal investment evaluated by a forward performance criterion in a stochastic factor market model, in which the probability measure that models future stock price evolutions is ambiguous. The forward performance process, as an adapted stochastic dynamic utility evolving forward in time, has been introduced and developed in [41]- [45] (see also [24] and [55], and more recently [2], [3], [6], [12], [23], [28], [33], [37], [39] and [51]). This new concept differs from the classical expected utility function, in which the objective is to solve a stochastic control problem in a backward way via dynamic programming principle.…”

Section: Introductionmentioning

confidence: 99%

A Game Theoretical Approach to Homothetic Robust Forward Investment Performance Processes in Stochastic Factor Models

Li¹,

Li²,

Liang³

2021

SIAM J. Finan. Math.

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This paper studies an optimal forward investment problem in an incomplete market with model uncertainty, in which the underlying stocks depend on the correlated stochastic factors. The uncertainty stems from the probability measure chosen by an investor to evaluate the performance. We obtain directly the representation of the homothetic robust forward performance processes in factor-form by combining the zero-sum stochastic differential game and ergodic BSDE approach. We also establish the connections with the risk-sensitive zero-sum stochastic differential games over an infinite horizon with ergodic payoff criteria, as well as with the classical robust expected utilities for long time horizons. Finally, we give an example to illustrate that our approach can be applied to address a type of robust forward investment performance processes with negative realization processes.

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“…A key feature is that the Hamiltonian H(t, x, p) is convex and coercive in p. In particular, this covers the case that H has quadratic growth in p, a case that corresponds to a rich class of equations in mathematical finance arising, for example, in optimal investment with homothetic risk preferences ( [18]), exponential indifference valuation ( [8,16,17]) and entropic risk measures ( [9]), just to name a few. Note that if u < f in Q T , equation (1.1) reduces exactly to the semilinear parabolic PDE considered in [19]:…”

Section: Introductionmentioning

confidence: 99%

An Approximation Scheme for Semilinear Parabolic PDEs with Convex and Coercive Hamiltonians

Huang¹,

Liang²,

Zariphopoulou³

2020

SIAM J. Control Optim.

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We propose an approximation scheme for a class of semilinear variational inequalities whose Hamiltonian is convex and coercive. The proposed scheme is a natural extension of a previous splitting scheme proposed by Liang, Zariphopoulou and the author for semilinear parabolic PDEs. We establish the convergence of the scheme and determine the convergence rate by obtaining its error bounds. The bounds are obtained by Krylov's shaking coefficients technique and Barles-Jakobsen's optimal switching approximation, in which a key step is to introduce a variant switching system.

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An ergodic BSDE approach to forward entropic risk measures: representation and large-maturity behavior

Cited by 25 publications

References 36 publications

Systems of Ergodic BSDEs Arising in Regime Switching Forward Performance Processes

Systems of Ergodic BSDEs Arising in Regime Switching Forward Performance Processes

A Game Theoretical Approach to Homothetic Robust Forward Investment Performance Processes in Stochastic Factor Models

An Approximation Scheme for Semilinear Parabolic PDEs with Convex and Coercive Hamiltonians

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