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We obtain a representation theorem for the generators of BSDEs driven by -Brownian motions and then we use the representation theorem to get a converse comparison theorem for -BSDEs and some equivalent results for nonlinear expectations generated by -BSDEs.
We investigate the tailed asymptotic behavior of the randomly weighted sums with increments with convolution-equivalent distributions. Our obtained result can be directly applied to a discrete-time insurance risk model with insurance and financial risks and derive the asymptotics for the finite-time probability of the above risk model.
For a mixed stochastic Volterra equation driven by Wiener process and fractional Brownian motion with Hurst parameter , we prove an existence and uniqueness result for this equation under suitable assumptions.