The problem of robust optimal investment with exchange rate risk and default risk is studied. We assume that investors are ambiguity averse and they have access not only to the domestic market but also to the foreign market. The corresponding Hamilton–Jacobi–Bellman (HJB) equations are first obtained through the robust stochastic optimal control theory. Then, we discuss the optimal investment problems before and after default, and the value functions and optimal investment strategies are obtained. Finally, we find that the optimal investment strategies of pre-default are affected by the intensity of default and the credit spread, and the investors cannot hold defaultable bonds in the post-default case. Numerical results also show that the exchange rate risk, default risk and ambiguity aversion have a great effect on the optimal investment strategies.

中文翻译：

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具有汇率风险和违约风险的稳健最优投资策略

研究了具有汇率风险和违约风险的稳健最优投资问题。我们假设投资者是模糊厌恶的，他们不仅可以进入国内市场，还可以进入国外市场。首先通过鲁棒随机最优控制理论获得相应的 Hamilton-Jacobi-Bellman (HJB) 方程。然后讨论违约前后的最优投资问题，得到价值函数和最优投资策略。最后，我们发现违约前的最优投资策略受违约强度和信用利差的影响，并且投资者在违约后的情况下不能持有可违约债券。数值结果还表明，汇率风险，