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math.PR2023
On the Absolute-Value Integral of a Brownian Motion with Drift: Exact and Asymptotic Formulae
Weixuan Xia, Yuyang Zhang
The present paper is concerned with the integral of the absolute value of a Brownian motion with drift. By establishing an asymptotic expansion of the space Laplace transform, we o…
math.PR2023
Set-valued stochastic integrals for convoluted Lévy processes
Weixuan Xia
In this paper we study set-valued Volterra-type stochastic integrals driven by Lévy processes. Upon extending the classical definitions of set-valued stochastic integral functional…
q-fin.MF2023
Optimal Consumption--Investment Problems under Time-Varying Incomplete Preferences
Weixuan Xia
The main objective of this paper is to develop a martingale-type solution to optimal consumption--investment choice problems ([Merton, 1969] and [Merton, 1971]) under time-varying…