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Forward Investment Performance Processes in Semimartingale Financial Markets. (arXiv:1811.11899v1 [math.PR])
来源于:arXiv
We analyze the forward performance process in a general semimartingale market
accounting for portfolio constraints, when investor's preferences are
homothetic. We provide necessary and sufficient conditions for the construction
of such a performance process, and establish its connection to the solution of
an infinite-horizon quadratic backward stochastic differential equation (BSDE)
driven by a semimartingale. We prove the existence and uniqueness of a solution
to our infinite-horizon BSDE using techniques based on Jacod's decomposition
and an extended argument of the comparison principle for finite-horizon BSDEs.
We show the equivalence between the factor representation of the BSDE solution
and the smooth solution to the ill-posed partial integral-differential
Hamilton-Jacobi-Bellman (HJB) equation arising in the extended semimartingale
factor framework. Our study generalizes existing results on forward performance
in Brownian settings, and shows that time-monotone processes are prese 查看全文>>