"On the effect of risky investments on the ruin probabilities of
by Sheng Lin
Abstract: In the classical models for the evolution of the capital reserve of an insurance company, the company was not assumed to earn any investment income. The ruin probability decays exponentially in that case as the initial capital approaches infinity. However, when investment with uncertain return is incorporated into the model, the decay rate is a power function. In particular, when the claim size is thin tailed, investment risk dominates the underlying insurance risk; this is reflected in the fact that the index of power decay function depends only on the parameter of the investment process. We review some key results associated with ruin probability under uncertain investment, derive an integro differential equation together with boundary conditions that must be satisfied by the ruin probability and provide some numerical illustrations.
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