Robust mean–variance hedging via <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml1" display="inline" overflow="scroll" altimg="si1.gif"><mml:mi>G</mml:mi></mml:math>-expectation

Biagini, Francesca; Mancin, Jacopo; Brandis, Thilo Meyer

doi:10.1016/j.spa.2018.04.007

Cited by 10 publications

(1 citation statement)

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“…In addition, the general sublinear expectation � IE and a particular G-expectation have been used to establish a new central limit theorem for G-normal distributions [78], and for the study dynamic risk measures [76,82]. Those results have been applied to contingent claim pricing in financial markets with uncertain volatility [41,95], as well as to stochastic control theory [97,44] and to the robust mean-variance hedging [10]. Recently, Song [87,88] has extended Stein's method to G-normal approximation under sublinear expectations.…”

Section: Introductionmentioning

confidence: 99%

Stochastic orderings by nonlinear expectations

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We study the theory of stochastic order under the nonlinear expectations framework, including g-and G-expectations, which leads to more general concepts of orderings in comparison with the standard linear expectation setting. The g-expectation E g is generated by a solution of Backward Stochastic Differential Equation (BSDE) and it provides a new robust tool for option pricing in finance. In the same manner, we denote by E G a nonlinear expectation generated by a solution of G-Backward Stochastic Differential Equation (G-BSDE), which is defined on G-expectation spaces. In this dissertation, our main contributions consist of four parts as follows:(i) We extend several properties of monotonicity, convexity and continuous dependence for the solutions of Forward-Backward Stochastic Differential Equations (FBSDEs) and associated semilinear parabolic Partial Differential Equations (PDEs). Also, we obtain analogous results for the solutions of G-Forward-Backward Stochastic Differential Equations (G-FBSDEs) and associated G-PDEs (Hamilton-Jacobi-Bellman-type equations). These properties are very crucial to constitute comparison results for the monotonic, convex, increasing convex g-and G-stochastic orderings.(ii) We give some characterizations for a better understanding of g-stochastic orderings which are defined via the g-evaluations and g-expectations E g . We then derive several sufficient conditions for the convex, increasing convex and monotonic g-stochastic orderings of diffusion processes at the terminal time T . Analogous comparison results for g-risk measures have been proposed as consequences, in terms of concave g-stochastic orderings. Applications of the g-stochastic orderings to contingent claim price comparison under different hedging portfolio constraints are also provided. (W t ) t≥0 Standard Brownian motion (B t ) t≥0 G-Brownian motion

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Section: Introductionmentioning

confidence: 99%

Stochastic orderings by nonlinear expectations

Ly¹

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Backward Stochastic Differential Equations Driven by G-Brownian Motion with Uniformly Continuous Generators

Wang

Zheng

2020

J Theor Probab

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The present paper is devoted to investigating the existence and uniqueness of solutions to a class of non-Lipschitz scalar valued backward stochastic differential equations driven by G-Brownian motion (G-BSDEs). In fact, when the generators are Lipschitz continuous in y and uniformly continuous in z, we construct the unique solution to such equations by monotone convergence argument. The comparison theorem and related Feynman-Kac formula are stated as well.

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Could we rely on credit swap hedging as a substitute for insurer blockchain technology involvement?

Lin

2022

International Review of Economics & Finance

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Robust mean–variance hedging via G-expectation

Cited by 10 publications

References 20 publications

Stochastic orderings by nonlinear expectations

Stochastic orderings by nonlinear expectations

Backward Stochastic Differential Equations Driven by G-Brownian Motion with Uniformly Continuous Generators

Could we rely on credit swap hedging as a substitute for insurer blockchain technology involvement?

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