An optimal portfolio problem with Default Risk
by Lijun Bo
Abstract: In this talk, we investigate a stochastic portfolio optimization problem with default risk. The default risk premium and the default intensity corresponding to the perputally defaultable bond are assumed to rely on a stochastic factor governed by a diffusion process. We study the optimal allocation and consumption policies to maximize the expectation of the discounted non-log HARA utility of the consumption, and we use the dynamic programming principle to derive the Hamilton-Jacobi-Bellman (HJB) equation. We then explore the HJB equation by employing a so-called sub-super solution approach. The optimal allocation and consumption policies are finally presented in a verification theorem.
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