Scenario Analysis for a Multi-Period Diffusion Model of Risk

This paper extends and develops the results of a previous paper Malinovskii (2007). Dealing with a simplistic diffusion multi-year model of insurance operations, this paper illustrates the adaptive control approach when the object of control is the balance of solvency and excellency. Compared to the previous paper, a new element is the "scenario of nature", or the incomplete knowledge of future risk, which is quite often the case in insurance. It introduces a new and inevitable randomness in the model and leads to a qualitative difference in its behavior.

Keywords: Multi-period insurance process, Diffusion annual mechanisms, Volatile scenario, Solvency, Equity, Adaptive control strategies.