Optimal stochastic control and optimal consumption and portfolio with G-Brownian motion

Abstract

By the calculus of Peng's G-sublinear expectation and G-Brownian motion on a sublinear expectation space $(\Omega ,\mathcal{H},\hat{\mathbb{E}})$, we first set up an optimality principle of stochastic control problem. Then we investigate an optimal consumption and portfolio decision with a volatility ambiguity by the derived verification theorem. Next the two-fund separation theorem is explicitly obtained. And an illustrative example is provided.

29 pages

References in corpus (1)

• Fractional G-White Noise Theory, Wavelet Decomposition for Fractional G-Brownian Motion, and Bid-Ask Pricing Application to Finance Under Uncertainty

Cited by in corpus (3)

• Consistency of least squares estimation to the parameter for stochastic differential equations under distribution uncertainty
• A Stochastic Maximum Principle for Processes Driven by G-Brownian Motion and Applications to Finance
• Model reduction and uncertainty quantification of multiscale diffusions with parameter uncertainties using nonlinear expectations