Ӧ�ø���ͳ�� 2014, 30(4) 353-371 DOI:      ISSN: 1001-4268 CN: 31-1256

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Optimal Consumption and Portfolio with Ambiguity to Markovian Switching
Yu Minxiu, Fei Weiyin, Xia Dengfeng
School of Mathematics and Physics, Anhui Polytechnic University
Abstract:

This paper considers the problem of maximizing expected
utility from consumption and terminal wealth under model uncertainty for a general
semimartingale market, where the agent with an initial capital and a random endowment
can invest. To find a solution to the investment problem we use the martingale method.
We first prove that under appropriate assumptions a unique solution to the investment
problem exists. Then we deduce that the value functions of primal problem and dual
problem are convex conjugate functions. Furthermore we consider a diffusion-jump-model
where the coefficients depend on the state of a Markov chain and the investor is
ambiguity to the intensity of the underlying Poisson process. Finally, for an agent
with the logarithmic utility function, we use the stochastic control method to derive
the Hamilton-Jacobi-Bellmann (HJB) equation. And the solution to this HJB equation can
be determined numerically. We also show how thereby the optimal investment strategy
can be computed.

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